



Number
list: lista
dei numeri (it), liste des nombres (fr), lista de números (es,
por), Liste besonderer Zahlen (ger), getallen en getalverzamelingen (du), seznam čísel (cz), 數表 (ch), 数の一覧 (jap), список чисел (ru), שמות מספרים (he).
06  712  1323  2469  70200  2012017  5H0P
13 
is
a Devil's dozen, or a baker's dozen,
also known as a long dozen (one more than a
proper dozen).
is the only integer that is, along with its fourth power, the sum
of two consecutive squares:
13 = 2^{2} + 3^{2} and
13^{4} = 119^{2} + 120^{2}
appears
for the first time at 111th place in decimal
expansion of (Pi):
3.141592653589793238462643383279502884197169399375105820974944
592307816406286208998628034825342117067982148086513...
is the
number of Archimedian
solids:
is the
sum and the difference of 2 consecutive squares:
13
= 2^{2 }+ 3^{2 }= 7^{2}  6^{2}
13 =
(1^{3}+ 3^{3})/2
13^{2 }=
5^{2} + 12^{2 }=
85^{2}  84^{2} (Pythagorean
triple)
13^{2 }= 8^{3}  7^{3} (Diophantine
equation)
13^{2 }= 7 + 8 + 9 + ... + 17
+ 18 + 19 (sum of consecutive numbers)
13^{2} divides
12! + 1
1
+ 2 + 3 + 4 + ... + 10 + 11 + 12 + 13 = 1^{2} +
2^{2} + 3^{2} + 4^{2} + 5^{2} +
6^{2}
If we
subtract the sum of its digits, we get a perfect square:
13  (1 + 3) = 9 = 3^{2}
If we add the product of its digits, we get another perfect square:
13 + (1 x 3) = 16 = 4^{2}
(10^{6 }
1)/13 = 27 x 37 x 77 and 77  37  27 = 13

by Gianni A. Sarcone 
1/13
= 0.076923076923076923... (rational
periodic infinite decimal)
On multiplying the periodic number 76923 by
successive multiples of 13, this curious numerical pattern is obtained:
76923
x 13 =
76923 x 26 =
76923 x 39 =
76923 x 52 =
76923 x 65 =
76923 x 78 =
76923 x 91 =
76923 x 104 =
76923 x 117 =
76923 x 130 = 
0999999
1999998
2999997
3999996
4999995
5999994
6999993
7999992
8999991
9999990 
A
scalene triangle having sides 13, 14 and 15
(consecutive integers) has an area that is also an integer (84
units^{2}). Such triangles whose
sidelengths and area are all integers are called Heronian
triangles.
 For more info on the Heronian triangles read the
interesting article by M. P. Cohen "Generating Heronian Triangles
with consecutive Integer Sides" in Journal
of Recreational Mathematics, Vol. 30(2) 121124.
is
the smallest prime that can grow 6 times by the right:
13 is prime,
139 is prime,
1399 is prime,
13999 is prime,
139991 is prime,
1399913 is prime,
13999133 is prime.
13,333,333,333,333
/ 13 = 1,025,641,025,641 (prime number!)
Palindromic
equalities involving 13:
13 x 62 = 26 x 31
13 x 93 = 39 x 31
13 x 13 = 169 and 961 = 31 x 31
(13 
1)! + 1 = 0 (mod 13^{2})
There
are two ways to pack neatly thirteen (13) circular
or spherical items in a rectangular space:
The
numerical pattern abcabc is
divisible by 13.
p^{12}  q^{12} is
divisible by 13 only when p and q are not divisible
by 13.
The
sum S(n) = 1^{4n+2 }+ 2^{4n+2} + 3^{4n+2 }+
4^{4n+2 }+ 5^{4n+2 }+ 6^{4n+2} is divisible
by 13 for any positive integer.
A
torus (kind of donut) can be sliced into 13 pieces
with just 3 plane cuts.
Number
anagram: ELEVEN + TWO = TWELVE + ONE
While
the Earth revolves once, the Moon revolves 13 times.
The
US flag displays 13 stripes  for the original 13 states.
The
average human bladder can hold 13 ounces of liquid.
'Magicicada'
life cycles
Periodical cicadas spend five juvenile stages in their underground
burrows, and during their 13 or 17 years
underground they grow from approximately the size of a small ant
to nearly the size of an adult. In the spring of their 13th or
17th year, a few weeks before emerging, the nymphs construct exit
tunnels to the surface. These exits are visible as approximately
1/2 inch diameter holes, or as chimneylike mud "turrets" the
nymphs construct over their holes. Sometimes a large proportion
of the cicada population emerges in one night!
Probability
There is always at least one Friday 13^{th} in each year.
The probability of being born on a Friday the 13th is about 1/214...
OK, but which day of the week (Sunday, Monday, etc.) is the probability
largest to fall on the 13th of a random month, in a random year?
(Or is this probability the same for each day of the week?)
No, the probability that the 13th of a certain month in a certain
year is a Friday, is slightly higher (at 688/4800). The probability
that the 13th of a certain month in a certain year is a Thursday
or a Saturday, is the lowest (at 684/4800).
 posted by Patrick Freymond 
Any
month that starts on a Sunday will have a Friday the 13th.
Any non leap year February that starts with a Sunday, there will
be a Friday the 13th in February and March...
According
to historians, there were 13 people at Christ's Last Supper and
Christ was crucified on Friday 13th. So, Friday 13th is considered
as unlucky... But thirteen may be considered a 'bad' number simply
because it is one more than 12, which is a popularly used number
in many cultures (due to it being a highly composite number).
When a group of 13 objects is divided into two, three, four or
six equal groups, there is always one object leftover.
The
fear of the number 13 is called 'Triskaidekaphobia'.
A specific fear of Friday the 13th is called Paraskavedekatriaphobia (from
Greek Παρασκευή Friday
+ δεκατρείς thirteen
+ phobia) or Friggatriskaidekaphobia. In the Spanishspeaking
world, it is Tuesday the 13th that brings bad luck... A proverb
runs "En martes, ni te cases ni te embarques" (on
Tuesday, neither get married nor start a journey).
"13bis,
estce un nombre pair ou impair?" (13bis  French road numbering
scheme  is an even or an odd number?)  R.Queneau,
'Le Vol d'Icare'
"Tirè el
trédas" (to draw the thirteen) means to
die in Piedmontese.
THIRTEEN in
different languages (© G.
Sarcone)
(Old English thrêotêne) 
Indoeuropean
 *TRÍDEKM(T) 
Sanskrit  trayodaśa 
Greek, Attic  τρεισκαίδεκα TRESKAIDEKA 
Latin  TREDECIM  
Italian tredici;
French treize; Spanish trece;
Portuguese treze; Catalan and Provençal tretze;
Romanian treisprezece (treişpe,
informal); Rumansh tredisch; Sardinian tréchi. 
Old
Germanic  THRI(S)TEHUN  
Dutch dertien;
German dreizehn; Danish and Norwegian tretten;
Swedish tretton; Icelandic þrettán. 
Old
Slavic  TRINADESETJE  
Russian тринадцать trinadtsat';
Czech třináct; Slovenian trinajst;
Polish trzynaście. 
Chinese 十三 (complex
form 拾参) shísān. 
Ancient
Egyptian met'khemte; Akkadian shalashsher(et). 
Arabic ثلاثة عشر thalatha'ashar;
Hebrew שלוש עשרה shlosh'esrei;
Maltese: tlettax; Amharic asrasost. 
More
languages
Magyar tizenhárom.
Mayan oxlahun.
Nahuatl mahtlāctli onēyi.
Suomi kolmetoista.
Zulu ishumi na tatu. 
Buy
your favorite
Number (13) here. 
14 
is
a product of 2 primes (2x7) and a repfigit
number.
is a Catalan
number. Catalan numbers are generated by the formula C_{n }=
[(2n)!/n!(n+1)!]
is a square
pyramidal number:
= 1 + 4 + 9 = 1^{2} + 2^{2} + 3^{2}
is the integer solution to: x^{2}  y^{2}  x  y =
30 [x = 16, and y = 14]
10^{14} 
(2 x 14  1) and 10^{14} 
(2 x 14 + 1) are 14digit twin
primes.
There
are only 14 prime
knots < order 7:
The cuboctahedron,
the truncated
cube, and the truncated
octahedron each have 14 faces.
= 13^{2} +
3^{3}
= 2 + 3 + 4 + 5 (summ of consecutive integers)
= 2^{1} + 2^{2} + 2^{3} (summ
of consecutive powers of 2)
= 7(16^{2}  14^{2})/(16 + 14)
= (log_{2}128)(log_{7}49)
1/14
= 0.0714285714285714285...
Curiously 7, 14,
and 28 are factors
and multiples of 14. The digit 5 tells you how
many digits 71428 has
before they repeat!
Arithmetic
curiosity: 14^{2} – 7^{2} =
(14 + 7)
x 7
The
squares of 13, 14 and 31 share the same digits:
13^{2} = 169;
14^{2} = 196;
31^{2} = 961
A fortnight has
14 days (i. e. two weeks, from Old English: feowertiene niht,
fourteen nights).
Most
people fart 14 times a day on average... ;)
February
14 is St Valentine's day.
CALENDAR
REFORM IN ENGLAND
In September 1752, Great Britain switched from the Julian Calendar
to the Gregorian Calendar. In order to achieve the change, 11 days
were 'omitted' from the calendar: the day after 2 September 1752
was 14 September 1752.
It
takes 14 days (one fortnight) for the Moon to wax from new to
full or to wane from full to new.
In
ancient Egypt, Osiris  the god of the afterlife  was cut into
14 parts. Each part represented one of the 14 full moons (each
year has in fact 12 to 14 full moons).
There
is a Finnish word that contains a continuous sequence of 14 dots: Pääjääjää ('the
main stayer' in Finnish, partitive case).
The
French expression: "chercher midi à quatorze heures" (to
look for noon at 14:00  i.e. 2 pm) is a quirky
way of telling someone that he is making an issue more difficult
than it needs to be  that is, turning something simple into
something complicated.
The
'Fourteen Words' is a phrase used by white nationalists.
It refers to the 14word slogan: "we must secure the existence
of our people and a future for white children". Often found
in combination with 88 (14/88, 8814...).
FOURTEEN in
different languages (© G.
Sarcone)
(Old English fêowertêne) 
Indoeuropean
 *K^{W}ETWORDEKM(T) 
Sanskrit  catúrdaśa 
Greek, Attic  τέτταρες καὶ δέκα TETTARES
KAI DEKA 
Latin  QVATTVORDECIM , Archaic
Latin  *QVATBORDECEM  
Italian quattordici;
French, Portuguese quatorze; Spanish catorce;
Catalan and Provençal catorze;
Romanian paisprezece (< patrusprezece);
Rumansh quitordisch; Sardinian batódighi. 
Old
Germanic  FITHWORTEHUN  
Dutch veertien;
German vierzehn; Danish and Norwegian fjorten;
Swedish fjorton; Icelandic fjórtján. 
Old
Slavic  CETYR(I)NADESETJE  
Russian четырнадцать chetyrnadtsat';
Czech čtrnáct; Slovenian štirinajst;
Polish czternaście. 
Chinese 十四 shísi. 
Ancient
Egyptian met'efte; Akkadian erbesher(et). 
Arabic أربعة عشر arba'a'ashar;
Hebrew ארבע עשרה arba'esrei;
Maltese: erbatax; Amharic asraarat. 
More
languages
Magyar tizennégy.
Mayan canlahun.
Nahuatl mahtlāctlinnāhui.
Suomi neljätoista.
Zulu ishumi na ne. 

15 
All
prime quadruplets  with only two exceptions  enclose a multiple
of 15, with 15 itself being enclosed by the quadruplet, e.g.:
11, 13, 17, 19.
is the
number of 3digit palindromic primes: 101, 131, 151, 181, 191,
313, 353, 373, 383, 727, 757, 787, 797, 919, and 929.
is a
triangular number: 1 + 2 + 3 + 4 + 5
is the positive solution to: 2x^{2}  27x = 45
15 and
21 are the smallest pair of triangular
numbers whose difference and sum are also triangular: 21
 15 = 6, and 21 + 15 = 36
= 3log_{2}32
= 4!
 !4 (substraction of factorial and subfactorial)
2^{4n }– 1 is divisible by
15.
3n^{5} +
5n^{3} +
7n is
divisible by 15.
=
8^{2} 
7^{2}
= 4^{2} 
1^{2}
15^{2} =
(1 + 2)(3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12)
15^{4} = 4^{4} + 6^{4} + 8^{4} +
9^{4} + 14^{4}
15,15 ≈ e^{e}
The
simpliest magic square having a 'magic constant' of 15:
is
the name of a famous slide puzzle: the 15
puzzle.
is the
number of 'The Devil' in the major arcana of Tarot cards.
A
penguin swims at a speed of approximately 15 miles per hour.
In
2007, Danish
sperm donors have helped to engender an estimated 15,000
children around the world!
15.23
is the hour of temptation. In fact, experts say it is the time
when it is most likely person to encroach on sweets... More
info at dietplanfortoday.com.
The
only 15letter word that can be spelled without repeating a letter
is "uncopyrightable".
In
the Hebrew
numeral system, the numbers 15 and 16 are
represented as (9+6)
and (9+7)
respectively, instead of (10+5)
and (10+6).
This is done in order to refrain from using the sacred combinations,
called tretragrammaton, that are a part of the name
of God in Judaism.
Huli,
a Papuan language spoken by the Huli
people of the Southern Highlands province of Papua New Guinea,
is known to have a quindecimal or pentadecimal (base15) numeral
system. For instance, the Huly people say "93" with ngui
waraga, ngui kanegonaga tebira, which means "(15 x
6) + (3 objects of the seventh 15)". The
number system of Huli.
FIFTEEN in
different languages (© G.
Sarcone)
(Old English fîftêne) 
Indoeuropean
 *PENK^{W}EDEKM(T) 
Sanskrit  pañcadaśa 
Greek, Attic  πεντεκαίδεκα PENTEKAIDEKA 
Latin  QVINDECIM  
Italian quindici;
French, Portuguese, Catalan, and Provençal quinze;
Spanish quince; Romanian cincisprezece (cinşpe,
informal); Rumansh quendisch; Sardinian bíndhichi. 
Old
Germanic  FIMFITEHUN  
Dutch vijftien;
German fünfzehn; Danish and
Norwegian femten; Swedish femton;
Icelandic fimmtán. 
Old
Slavic  PE^{n}TINADESETJE  
Russian пятнадцать pyatnadtsat’ ;
Czech patnáct; Slovenian petnajst;
Polish piętnaście. 
Chinese 十五 (complex
form 拾伍) shíwǔ. 
Ancient
Egyptian metti'ue; Akkadian hamishsher(et). 
Arabic خمسة عشر khamsa'ashar;
Hebrew חמש עשרה khamesh'esrei;
Maltese: ħmistax; Amharic asraamist. 
More
languages
Magyar tizenöt.
Mayan holahun.
Nahuatl caxtōlli.
Suomi viisitoista.
Zulu ishumi na nhlanu. 
Buy
your favorite
Number (15) here.

16 
is
the only integer of the form x^{y}=y^{x} with
x y
(2^{4}=4^{2}).
is the smallest number with exactly five divisors.
= 1
+ 3 + 5 + 7 (sum of the four first odd numbers)
= 128^{4/7}
16 +
9 = 25 = 5^{2}
16 x 9 = 144 = 12^{2}
Mathematically
correct result derived by incorrect calculation method (anomalous
cancellation):
16 = 16 = 1
64 64 4
The base
16 notational system for representing real numbers,
called hexadecimal, is particularly
important and used extensively in computer science, since four
bits (each consisting of a 'one' or 'zero') can be succinctly
expressed with just a single hexadecimal digit. The 16 distinct
digits used to represent numbers in hexadecimal notation are:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F.
The
human eye sees continuous motion at between 16 and
20 frames per second.
There
are 16 orders of mammals.
Romanian
constructs the names of the numbers 11 to 19 by a regular pattern
which could be translated as 'oneoverten', 'twooverten',
etc. All the other Romance
languages use a pattern like 'oneten', 'twoten', etc. for
11 to 15; and the pattern 'tenandseven', 'tenandeight', 'tenandnine'
for 17 to 19. For 16, however, they split into
two groups: some use 'sixten', while others use 'tenandsix':
• 'Sixteen': French seize, Italian sedici, Catalan
and Occitan setze, Sardinian sédichi.
• 'Ten and six': Portuguese dezasseis or dezesseis,
Spanish dieciséis.
• 'Six over ten': Romanian şaisprezece (where spre derives
from Latin 'super').
SIXTEEN in
different languages (© G.
Sarcone)
(Old English siextiêne) 
Indoeuropean
 *SEKSDEKM(T) 
Sanskrit  ṣoḍaśa 
Greek, Attic  ἑκκαίδεκα HEKKAIDEKA 
Latin  SEDECIM  
Italian sedici;
French seize; Catalan, and Provençal setze;
Spanish dieciséis (< diez
y seis); Portuguese dezasseis or dezesseis;
Romanian şaisprezece (saişpe,
informal); Rumansh sedisch; Sardinian sédichi. 
Old
Germanic  SEKSTEHUN  
Dutch zestien;
German sechzehn; Danish and Norwegian seksten;
Swedish sexton; Icelandic sextán. 
Old
Slavic  S^{h}ESTINADESETJE  
Russian шестнадцать shestnadtsat’ ;
Czech šestnáct; Slovenian šéstnajst;
Polish szesnaście. 
Chinese 十六 (complex
form 拾陆) shíliù. 
Ancient
Egyptian mettise; Akkadian sheshsher(et). 
Arabic ستة عشر sitta'ashar;
Hebrew שש עשרה shesh'esrei;
Maltese: sittax; Amharic asrasidist. 
More
languages
Magyar tizenhat.
Mayan uaclahun.
Nahuatl caxtōloncē.
Suomi kuusitoista.
Zulu ishumi ne situpa. 

17 
17
and 19 form a twin
prime pair.
is the 7^{th} prime number and the only prime of the form p^{q} + q^{p},
where p and q are prime: 17 = 2^{3} + 3^{2}
is also the only prime number which is the sum of 4 consecutive
primes:
17 = 2 + 3 + 5 + 7
is the smallest number with four representations as a sum of three
primes: 17 = 2 + 2 + 13 = 3 + 3 + 11 = 3 + 7 + 7 = 5 + 5 + 7
is the lowest number that can be written as A^{3} + B^{2} in
2 distinct ways:
17 = 2^{3} + 3^{2} and 17 = 1^{3} + 4^{2}
is a
'cult number'  a number which has an unusually large number
of fans. Cult numbers are related to 'psychologically
random numbers', i.e. numbers which are chosen more often
when someone is asked to pick a random number.
is the
lowest possible number of givens for a Sudoku puzzle (数独)
with a unique solution (this was proven in 2012 by Gary McGuire,
Bastian Tugemann, and Gilles Civario).
abcdefghabcdefgh is
divisible by 17 (replace each letter with a digit. E.g. 1234567812345678).
The reason is that any number of that form is a multiple of 100,000,001
 which is divisible by 17.  David Grossberg
The
multiplicative inverse of 17 gives a decimal
expansion with a 16digit repeating decimal:
1/17=0,05882352941176470588235294117647...
17
= 9^{2}  8^{2 }= 3^{4}  4^{3}
n^{2} + n +
17 = Prime, for n = 0 to 15
17 x
65,359,477,124,183 = 1,111,111,111,111,111
17^{2} can
be expressed as the sum of 1, 2, 3, 4, 5, 6, 7, 8 distinct squares.
17^{2} =
8^{2} + 15^{2} (primitive
Pythagorean triple)
17^{2} = 1^{3} + 2^{3} + 4^{3} +
6^{3}
17^{2} = 0^{0} + 1^{1} + 2^{2} +
3^{3} + 4^{4}
17^{3} = 47^{2} + 52^{2} = 17^{2} +
68^{2}
17^{3} = 4,913 and 4 + 9 + 1 + 3 = 17
17^{4} = 1^{4} + 4^{4} (first
sum of 2 distinct fourth powers)
17^{3} =
4,913 = (4 + 9 + 1 + 3)^{3}
17^{4} = 83,521 = (8 + 3 + 5 + 2 – 1)^{4}
17^{6} = 24,137,569 = (24 – 13 + 75 – 69)^{6}
_{=
2}2^{2}_{+
1 (Fermat
prime)}
A
regular 17gon can be constructed by using rule and compasses only.
There
are 17 ways to express 17 as the sum of one or more primes; 17
is the only integer that is equal to the number of prime partitions
of itself.
There
are almost 17 ounces in a pound.
The Alhambra,
a Moorish castle in Spain contains 17 different tiling
patterns, which is actually the total number of possible
tilings by translating and rotating geometric patterns. These
17 possible plane symmetry groups are better known as wallpaper
groups (see diagram below).
There
are seventeen 17 in the first thousand digits
of pi's decimal expansion.
A hypercube must
be cut along 17 faces to unfold into a threedimensional cross.
Magic
triangles: the digits 1 through 9 are arranged on a triangle
so that there is one digit on each vertex and two digits on each
side between the vertices. The total of the four digits on any
given side must equal 17.
Plutarch (Greek: Πλούταρχος),
the most famous biographer of the ancient world, records "The
Pythagoreans also have a horror for the number 17, for 17 lies
exactly halfway between 16, which is a square, and the number
18, which is the double of a square, these two, 16 and 18, being
the only two numbers representing areas for which the perimeter
equals the area (16 = 4 + 4 + 4 + 4 = 4 x 4 and 18 = 3 + 3 +
6 + 6 = 3 x 6)".
The
famous problem of the 17 camels: a sheik
has 3 children and owns 17 camels. His will stipulates that
the eldest is to receive half his property; the second son
is to receive the third of his property; and the third one,
the ninth of his property. On his death, how would the sons
share out the inheritance? Solution: They borrow a camel, share
out, and give back the camel: (17+1)/2 + (17+1)/3 + (17+1)/9
= 17 camels
(ref. Gaston Boucheny, "Curiosités et Récréations
Mathématiques". Paris, 1939)
Another
wellknown problem involving 17: x and y are integers between
2 and 100. Alex knows S = x+y, and Pat knows P = xy, but they
do not know x and y. "I can't calculate them" Pat
says, "I knew" Alex says. "So I know these two
numbers" Pat says, "In this case, so do I" Alex
concludes. Solution: S = 17 = 13 + 4
Autoreferential
growth rate: an enterprise growing at the rate of exactly 17.65717%
per year will become exactly 17.65717 times larger in exactly 17 years,
seven months, 29 days, and 21 hours... Which is exactly 17.65717
years!  Source: niquette.com.
On
'Yellow
Pigs Day' (July 17) in 1717, Handel's Water
Music was first performed.
is
the average
brain weight of a marmot (in grams).
Number
17 is a 1932 crime film directed by Alfred
Hitchcock. It was based on the play 'Number 17' by Joseph
Jefferson Farjeon. The film is about a group of criminals
who committed a jewel robbery and put their money in an old
house over a railway leading to the English Channel.
A
day on Uranus lasts for 17 hours.
17
is the number of syllables in a haiku.
A haiku consists of three line; 5 syllables in the first one,
7 syllables in the second and finally 5 syllables in the third
line.
March
17th is Saint Patrick Day, the patron Saint of Ireland. A common
symbol is the threeleaved shamrock. It is told that Saint Patrick
used the shamrock to explain the Holy Trinity.
Most
Italians believe that 17 is
unlucky, and they are very superstitious concerning it! For
instance, Alitalia airplanes have no 17th row [editor's
note: are you sure?], Italian buildings do not
have a seventeenth floor (in some hotels and apartment buildings
the room number '17' is replaced with '16bis'), and when the
Renault R17 went to Italy, it's name was changed to R117. Part
of the reason that Italians do not like 17 comes from their Latin
heritage. In fact, XVII rearranged spells VIXI, which means "I
am defunct (dead)" in Latin. The fear of the number 17 is
called 'heptadecaphobia' or 'heptakaidekaphobia'
(see below).
17
is a swear word in Swedish. The origin is still debated, and
is commonly used as "sjutton också!" (seventeen,
too!).
SEVENTEEN in
different languages (© G.
Sarcone)
(Old English seofontiêne) 
Indoeuropean
 *SEPT^{E}MDEKM(T) 
Sanskrit  saptadaśa 
Greek, Attic  ἑπτακαίδεκα HEPTAKAIDEKA 
Latin  SEPTEMDECIM (or SEPTENDECIM)
 
Italian diciassette (< dece
ac septe); French dixsept; Spanish diecisiete (< diez
y siete); Portuguese dezassete or dezessette;
Catalan disset; Provençal dètzesèt;
Romanian şaptesprezece (şapteşpe,
informal); Rumansh gissiat (siat =
7); Sardinian decassète. 
Old
Germanic  SIBUNTEHUN  
Dutch zeventien;
German siebzehn; Danish and Norwegian sytten;
Swedish sjutton; Icelandic sautján. 
Old
Slavic  SEDMINADESETJE  
Russian семнадцать semnadtsat’ ;
Czech sedmnáct; Slovenian sédemnajst;
Polish siedemnaście. 
Chinese 十七 (complex
form 拾柒) shíqî. 
Ancient
Egyptian metsafkhe; Akkadian shebesher(et). 
Arabic تسعة عشر sab'a'ashar;
Hebrew שבע עשרה shva'esrei;
Maltese: sbatax; Amharic asrasebat. 
More
languages
Magyar tizenhét.
Mayan uuclahun.
Nahuatl caxtōlomōme.
Suomi seitsemäntoista.
Zulu ishumi ne sikhombisa. 
Buy
your favorite
Number (17) here.

18 
is
the area and also the perimeter of a rectangle with 6 and 3unit
sides.
is the only number that is twice the sum of its digits.
= 3
+ 4 + 5 + 6 (sum of consecutive numbers)
= 3^{3}  3^{2}
= (2
+ 8)^{2
}= CM/L
18 _{=} 9
+ 9
81 9
x 9
18^{2} =
6^{2} + 22^{2 } 14^{2} = 7^{2} +
30^{2 } 25^{2}
18^{3} =
5832 and 5 + 8 + 3 + 2 = 18
18^{3} = 5832
18^{4} = 104976 (both
results together include all digits once)
18
equilateral triangles make a hexagon ring.
is
the solution to the classic puzzle: "my age today is three
times what it will be three years from now minus three times
what my age was three years ago. How old am I?" [x = 3(x
+ 3)  3(x  3)].
is the
number of people it takes to consume the amount of oxygen created
by an acre of trees each year.
is approximately
the numbers of years of one Saros
cycle. The Saros cycle is an eclipse cycle with
a period of 223 synodic months (near 18 years +
11 1/3 days), useful to predict eclipses of the Sun and Moon.
One cycle after an eclipse, the Sun, Earth, and Moon return to
the same relative geometry, and a nearly identical eclipse will
occur. The coincidence of the Saros cycle was discovered by the
Babylonian.
is a
hate number symbol. The first letter of the alphabet is 'A';
the eighth letter of the alphabet is 'H'. Thus, 1 plus 8, or
18, equals 'AH', an abbreviation for Adolf Hitler. NeoNazis
use 18 in tattoos. The number is also used by "Combat
18", a violent British neoNazi group that chose its name
in honor of Adolf Hitler. The number 18 is also considered a
number of the devil due to the fact that 6+6+6=18, and 666 is
the Number of the Beast.
On
Earth, the length of a day 900 million years ago was only about 18 hours.  Science
magazine
Another
interesting Finnish word that contains a sequence of 18 dots: Pääjäävääjää ('the
main waiver' in Finnish, partitive case).  posted
by Juhani Sirkiä 
DIECIOCHO (=
18), is the largest Spanish number written in capital letters
that has horizontal symmetry (i.e. the top is a mirror image
of the bottom).
The
18letter words 'conservationalists' and 'conversationalists'
are anagrams of each other. They are the longest pair of anagrams
with such properties.
There
are 18 chapters in the Hindu epic tale Bhagavad
Gita.
A
fetus develops fingerprints at
18 weeks.
According
to the system of 'gematria',
the word for "life" in Hebrew (see chai)
is composed of two letters whose numerical value is 18. For this
reason, 18 is a lucky number in Judaism, and many Jews give gifts
of money in multiples of 18 for good luck.
EIGHTEEN in
different languages (© G.
Sarcone)
(Old English e(a)htatêne) 
Indoeuropean
 *OKTODEKM(T) 
Sanskrit  aṣtadaśa 
Greek, Attic  ὀκτωκαίδεκα OKTÔKAIDEKA 
Latin  OCTODECIM or DVODEVIGINTI  
Italian diciotto (< dece
ac octo); French dixhuit; Spanish dieciocho (< diez
y ocho); Portuguese dezoito; Catalan divuit;
Provençal dètzeuèch;
Romanian optsprezece (optişpe, optîşpe,
or opşpe, informal); Rumansh schotg (otg =
8); Sardinian decheòto. 
Old
Germanic  AHTÔTEHUN  
Dutch achttien;
German achtzehn; Danish and Norwegian atten;
Swedish arton or aderton;
Icelandic átján. 
Old
Slavic  OS(T)MINADESETJE  
Russian восемнадцать vosemnadtsat’ ;
Czech osmnáct; Slovenian ósemnajst;
Polish osiemnaście. 
Chinese 十八 (complex
form 拾捌) shíbā. 
Ancient
Egyptian metkhmune; Akkadian samansher(et). 
Arabic ثمانية عشر thamaniya
'ashar; Hebrew שמונה עשרה shmone'esrei;
Maltese: tmintax; Amharic asrasemment. 
More
languages
Magyar tizennyolc.
Mayan uaxaclahun.
Nahuatl caxtōlonēyi.
Suomi kahdeksantoista.
Zulu ishumi ne sishiyagalombili. 

19 
is
a prime and a repfigit
number.
is the maximum number of 4^{th} powers needed to sum to
any number.
19/7
is a good rational approximation of the constant e (Euler's
number, or Napier's constant).
It
is possible to arrange 12 coins into 19 rows
of 3 coins each.
The
integers 19, 109, 1009, 10009 are prime and the next is 1000000009.
The
multiplicative inverse of 19 gives a decimal
expansion with a 18digit repeating decimal:
1/19=0,052631578947368421052631578947368421...
This repeating decimal has also an interesting property: in fact,
to multiply the number 105,263,157,894,736,842
by two, you just have to move the last digit 2 to
the beginning of the number: 210,526,315,789,473,684.
Numbers having such properties are called parasitic
numbers.
With
respect to divisibility, nineteen has a very simple test: 19
divides 100a + b if, and only if, it divides a +
4b.
A
number abc (= 100a + 10b + c)
is divisible by 19 if, and only if, 10a + b +
2c is. Example: 475 > 47 + 2x5 = 57 = 3
x 19, so 475 is divisible by 19.
Any
number abcdefghiabcdefghi is
divisible by 19. Example:
123456789123456789 / 19 = 6497725743339831
The
sum 2^{2n}+3^{2n}+5^{2n} is
always divisible by 19 and the sum 2^{4n}+3^{4n}+5^{4n} is
always divisible by 19^{2} for any integer n^{3}.
19
= 1 x 9 + 1 + 9, and 29 = 2 x 9 + 2 + 9. This also works for
39, 49, 59, 69, 79, 89 and 99.
1
+ 2 + 3 + ... + 17 + 18 + 19 = 19 x
10
=
1^{2} + 3^{2} + 3^{2} (sum
of squares)
= 10^{2}  9^{2} (difference of
consecutive squares)
= 3^{3}  2^{3} (difference of consecutive
cubes)
=
32  3^{2}  2^{2}
= 53  5^{2}  3^{2}
= 72  7^{2}  2^{2}
19^{3} =
27^{2} + 37^{2} + 69^{2}
=
 (1!) + 2!  (3!) + 4!
=
F + 4 (base 16)
Mathematically
correct result derived by incorrect calculation method (anomalous
cancellation):
19 = 19 = 1
95 95 5
The
unique possible Magic
Hexagon contains consecutive integers from 1 to 19 (see
image below). The numbers in each row, and in all three directions,
sum to the same magic constant: 38.
is
the smallest prime that can grow 8 times by the right:
19 is prime,
197 is prime,
1979 is prime,
19793 is prime,
197933 is prime,
1979339 is prime,
19793393 is prime,
197933933 is prime,
1979339339 is prime.
19
is the largest prime number that is palindromic in Roman numerals
(XIX).
Kelvin
Ship Waves Constant: Wakes fan out at a constant angle
of about 19.5°, no matter the speed of
the vessel.
The Rhind
Mathematical Papyrus (RMP) contained a problem to find
x so that x + x(1/7) = 19. (A quantity plus
oneseventh of it becomes 19. What is the quantity? Answer:
16 + 5/8)
Oktoberfest fact:
How many steins of beer can a waitress carry at one time? In
November 2008, Bavarian Anita Schwarz set a new world record
when she carried 19 full beer steins (5 in either
hand and 9 on top) totaling 45 kg.
19 is
the number of vertical and horizontal lines of a Go board (or "goban").
In fact, the board is always slightly longer than it is wide. "Go" comes
from Japanese igo 囲碁 which in turn comes
from Chinese wéiqí 圍棋, meaning: "encircling
game". Go is called baduk 바둑 in Korea,
and cờ vây in Vietnam.
"Nineteen" is
the term used to describe a worthless hand in the game of cribbage.
Number
19 plays an important role in the structure of the Quran (القرآن alqurʾān).
The numerical value of the Arabic word واحد (wahid),
which means "One", is 19. Thus, number 19 represents the 'Oneness
of God' which is a very important doctrine in Islam.
"The
Sun" is numbered with 19 in Tarot cards.
NINETEEN in
different languages (© G.
Sarcone)
(Old English nigontȳne) 
Indoeuropean
 *NEWNDEKM(T) 
Sanskrit  navadaśa or ekonavimśati (20
less 1) 
Greek, Attic  ἐννεακαίδεκα ENNEAKAIDEKA 
Latin  UNDEVIGINTI (20 less
1)  
Italian diciannove (< dece
ac nove); French dixneuf; Spanish diecinueve (< diez
y nueve); Portuguese dezanove or dezenove;
Catalan dinou; Provençal dètzenòu;
Romanian nouăsprezece (nouăşpe,
informal); Rumansh scheniv (niv =
9); Sardinian decannòbe. 
Old
Germanic  NIWUNTEHUN  
Dutch negentien;
German neunzehn; Danish and Norwegian nitten;
Swedish nitton; Icelandic nítján. 
Old
Slavic  DEVETINADESETJE  
Russian девятнадцать devyatnadtsat’ ;
Czech devatenáct; Slovenian devétnajst;
Polish dziewiętnaście. 
Chinese 十九 (complex
form 拾玖) shíjiǔ. 
Ancient
Egyptian metp'site; Akkadian or tishêret. 
Arabic تسعة عشر tisha
'ashar; Hebrew תשעה עשרה tsha'esrei;
Maltese: dsatax; Amharic asrazethain. 
More
languages
Magyar tizenkilenc.
Mayan bolonlahun.
Nahuatl caxtōlonnāhui.
Suomi yhdeksäntoista.
Zulu ishumi ne sishiyagalolunye. 

20
XX 
is
a tetrahedral
number and a composite
number (its proper divisors being 1, 2, 4, 5 and 10).
is also the number of rooted
trees with 6 vertices.
is the
base of the ancient Mayan numeral
system. The vigesimal or 20base numeral system is also present
in some number names in many different languages, such as:
French, quatrevingts, "four twenty" = 80; Danish, tres (short
for tresindstyve), "three times twenty" = 60;
Albanian, dyzet, "two twenties" = 40; Georgian, samotsdashvidi, "threetwentyandseven" =
67; Basque, hirurogeita hamabost, "threescoreandtenfive" =
75; Ainu, tu hotnep, "two twenties" = 40; Yoruba
(Nigerian language), métadinlaaadota, "three
from ten from twenty three", i.e. "3 from [10 from (20
x 3)]" = 47; English, four score = 80. 
G. Sarcone
=
1 + 1 + 2 + 3 + 5 + 8 (sum of the first 6 Fibonacci
numbers)
= 2 + 4 + 6 + 8 (sum of the first 4 even numbers)
= 1 + 3 + 6 + 10 (sum of the first 4 triangular
numbers)
=
2^{2} + 2^{2x2
}= 4(4/4 + 4)
= 6! / 6^{2}
≈ e  (very
very close to 20)
20
= 6^{2}  4^{2}
20^{2} = 29^{2}  21^{2 }= 7^{0 }+
7^{1 }+ 7^{2} + 7^{3
}20^{3} = 7^{3} + 14^{3} + 17^{3 }=
11^{3} + 12^{3} + 13^{3 }+ 14^{3 }(consecutive
cubes)
In
geometry, a regular icosahedron is a solid with
an equilateral triangle on each of its 20 faces. It is not possible
to make a regular polyhedron with more than 20 faces.
Magic
triangle with a constant of 20. 126 is the sum
of the squared numbers on any side.
20
is the number of pharmacist's drops in one milliliter.
The
bamboo flowers at the end if its life cycle  which for bamboo
is about every 20 to 120 years!
20
= 8 PM
1 meter
corresponds approximately to 1/(20 x 10^{6})
of the Earth Meridian.  posted by Hassan Taifour
20th
April
At 20:02 on Wednesday, April 20, 2002, it was 20:02
20/02 2002, (palindromic
date) in most European countries. 20:02 20/02 2002 is
a palindromic date because it is the same read from left to right
as it is read from right to left!
'20/20 vision'
is a term used to express normal visual acuity (the clarity or
sharpness of vision) measured at a distance of 20 feet. If you
have 20/20 vision, you can see clearly at 20 feet what should
normally be seen at that distance.
A
set of 20 units may also be referred to as a score.
'Nebuchadnezzar'
is a huge wine bottle holding the equivalent of 20 normal
bottles of wine.
The
word 'hussar' (obsolete; horseman of the Hungarian light cavalry)
meant originally "twentyworth". In
fact, in the 16th century, the Hungarian King Mathias Corvinus
decreed that each group of 20 households in a town was to furnish
a horse soldier, properly a huszár ('twentieth',
from Magyar húsz, 20)...
Read
carefully the 20word long sentence below:
"I do not know where family doctors acquired illegibly perplexing handwriting
nevertheless, extraordinary pharmaceutical intellectuality counterbalancing indecipherability,
transcendentalizes intercommunications incomprehensibleness".
This is a special sentence where the Nth word is N letters
long!
e.g. the 4rd word is 4 letters long, the 13th word is 13 letters
long, and so on.
In
any population, there are always nearly 20 percent of
people that are “contrary Mary”, that is persons
marked by a disposition to oppose and contradict, who are always
in contrast to any opinion taken by the majority or to opinions
that are largely accepted.
There
are 20 perfect interlingual homographs (words
that share the same spelling and meaning in French, English,
German, Italian, Spanish, etc...): album, diesel, embargo, gangster,
hotel, jazz, jockey, karate, laser, libido, mafia, matador, motel,
paranoia, radar, radio, revolver, sauna, taxi, telex, virus,
yoga.  G. Sarcone
TWENTY in
different languages (© G.
Sarcone)
(Old English twentig) 
Indoeuropean
 *WIK'MT(I) 
Sanskrit  vimśati 
Greek, Attic  εἴκοσι(ν) ÊKOSI(N) (< wikati,
cf. Doric ϝίκατι)

Latin  VIGINTI , Archaic Latin  *DVICINTI  
Italian venti;
French vingt; Spanish veinte;
Portuguese vinte; Catalan, and
Provençal vint; Romanian douăzeci;
Rumansh vegn; Sardinian bínti. 
Old
Germanic  *TWAI(GEN)TIGUS  
Dutch twintig;
German zwanzig; Danish and Norwegian tyve;
Swedish tjugo; Icelandic tuttugu. 
Old
Slavic  D(U)VADESETI  
Russian двадцать dvadtsat’ ;
Czech dvacet; Slovenian dvajset;
Polish dwadzieścia. 
Chinese 二十 èrshi or 廿 niàn (complex
form 貳拾 or 念). 
Ancient
Egyptian [ḏbˁ.ty] ḏubāʕatay;
Akkadian eshra. 
Arabic عشرون 'ishrun;
Hebrew עשרים esreem;
Maltese: għoxrin; Amharic haya. 
More
languages
Magyar húsz.
Mayan hunkal.
Nahuatl cempōhualli.
Suomi kaksikymmentä.
Zulu amashumi amabili. 
Buy your favorite
Number (20) here.

21 
is
the 3rd star number (3 x 3 + 4 x 3).
is a Fibonacci number, and
the smallest number of differently sized squares that
are needed to tile a square (see
below).
is the number of spots on a standard cubical die (1+2+3+4+5+6).
is the number of ways of choosing a set of 5 elements from a set
of 7 elements.
is x for: y=2x22 and 3x4y+17=0
= 11^{2} 
10^{2 }= 5^{2}  2^{2} (differences
of two squares)
= 1^{2} + 2^{2} + 4^{2} (sum
of three squares)
= 4^{0} + 4^{1} + 4^{2
}= 6^{2}  5^{2} + 4^{2}  3^{2} +
2^{2 } 1^{2
}= CV/V
=
2 + 2 + 17 = 3 + 5 + 13 = 3 + 7 + 11 = 5 + 5 + 11 = 7 + 7 + 7 (the
smallest number with 5 representations as a sum of 3 primes)
If
a square number ends with xyxyxyxyxy,
then xy =
21, 29, 61, 69 or 84. For instance: 508,853,989^{2} =
258932382121212121
2^{21} 
21 is prime.
21 is
the fewest number of distinct integersided squares needed to
tile a square. The simple perfect
squared square shown below was discovered by A. J. W. Duijvestijn
in 1976  Journal of Combination Theory.
"When
I Was OneandTwenty" is a dramatical verse by Alfred
Edward Housman about the futility of love, youth, experience,
and the irony in living life.
'Twentyone'
is the name of a card game (also called 'blackjack').
According
to the Mayan numerology December 21,
2012 (13.0.0.0.0, 4 Ajaw, 3 K’ank’in in Mayan reckoning)
is the end of the world.
 You can purchase our nice doomsday TShirts here.
 More
info about the Mayan prophecy.
The
German 'TwentyOne Club' (Zwanzigeins
e. V.) is dedicated to the promotion of a new way to spell
numbers in order to make mental arithmetic easier. The supporters
of the club want Germans to say zwanzigeins (twentyone)
instead of the current einundzwanzig (oneandtwenty).
TWENTYONE in
different languages (© G.
Sarcone)
(Old English ān and twentig) 
Indoeuropean
 *WIK'MTI OINOS(K^{w}E) 
Sanskrit  ekavimśati (1
+ 20) 
Greek, Attic  εἷς καὶ εἴκοσι(ν) HES
KAI EKOSI(N) (1 + 20) ,
or
 εἴκοσι (καὶ) εἷς EKOSI
(KAI) HES (20 + 1) 
Latin  UNUS (A, UM) ET VIGINTI (1 & 20) ,
or  VIGINTI UNUS, A, UM (20
+ 1)  
Italian ventuno;
French vingtetun; Spanish veintiuno;
Portuguese vinte e um; Catalan vintiu;
Provençal vinteun; Romanian douăzeci şi
unu (douăzeşunu,
informal); Rumansh ventgin; Sardinian bintúnu. 
Old
Germanic  *AINAZ (UNTA) TWAI(GEN)TIGUS (1 & 20)  
Dutch eenentwintig;
German einundzwanzig; Danish and
Norwegian enogtyve; Swedish tjugoett;
Icelandic tuttugu og einn. 
Old
Slavic  D(U)VADESETI I JEDINU  
Russian двадцать один dvadtsat’ odin;
Czech jedenadvacet, or dvacet
jeden; Slovenian ênaindvajset;
Polish dwadzieścia jeden. 
Chinese 二十一 èrshíyī (complex
form 貳拾壹). 
Ancient
Egyptian ḏubā'ataywie;
Akkadian ishten
(u) eshra (1 & 20). 
Arabic واحد و عشرون wahed
wa'ishrun (1 & 20);
Hebrew עשרים ואחת esreem
ve'akhat (20 & 1);
Maltese: wieħed u għoxrin;
Amharic haya and. 
More
languages
Magyar huszonegy.
Mayan hunkal catac hun.
Nahuatl cēmpōhualoncē.
Suomi kaksikymmentäyksi.
Zulu amashumi amabili na nye. 

22 
is
a pentagonal number (22 = 1 + 4 + 7 + 10) and a centered
heptagonal number.
is the number of partitions of
8. There are, in fact, precisely 22 ways to express
8 as a sum of positive integers: 8, 7+1, 6+2, 6+1+1, 5+3, 5+2+1,
5+1+1+1, 4+4, 4+3+1, 4+2+2, 4+2+1+1, 4+1+1+1+1, 3+3+2, 3+3+1+1,
3+2+2+1, 3+2+1+1+1, 3+1+1+1+1+1, 2+2+2+2, 2+2+2+1+1, 2+2+1+1+1+1,
2+1+1+1+1+1+1, and 1+1+1+1+1+1+1+1
is the
smallest number which can be expressed as the sum of 2 primes
in 3 ways: 3 + 19, 5 + 17, and 11 + 11
is the smallest number of differently sized squares that
are needed to tile a '2a x 1a' rectangle.
is the number of different ways of linking 5 hexagons together
(pentahexes,
see image below).
22/7
= 3.142... Honest approximation
of .
22 = κβ (in Ionic Greek
numeration)
= 4
+ 5 + 6 + 7
= 1^{4} + 2^{3} + 3^{2} + 4^{1
}= MC/L^{ }
22
x 22 = 4 x 11 x 11 = 484 is a palindromic equality!
"22
v'là les flics" is a French popular expression used
to warn of the coming of the police.
The
Olivetti "Lettera 22" is a portable
mechanical typewriter designed by Marcello Nizzoli in 1949. It
is in the permenant collection of the MOMA.
In
numerology, 22 is considered a significant number, sometimes
called the Master Builder or Spiritual Master in Form. Number22
persons are said to find themselves feeling as if they live in
2 worlds, one which is overwhelmed by the mundane, and the other
by the fantastic; they find the most fulfillment working on a
higher plane to help people.

23 
23
is the smallest odd prime which is not a twin
prime.
is one
of only two positive integers which CANNOT be written as the
sum of 8 positive cubes (239 is the other one).
 Christopher Carl Heckmann (23
letters!)
is the
smallest prime number with consecutive digits.
is the lowest prime whose reversal is a power: 32 = 2^{5} 
Trigg
is the lowest number of integersided parallelepipeds you can fit
in a box so that no two parallelepipeds share a common length.
occurs twice in the list of the fortunate
numbers.
Palindromic
equalities involving 23:
23 x 64 = 46 x 32
23 x 96 = 69 x 32
23!
is 23 digits long.
= 5 + 7 + 11 (smallest prime that is a sum of 3
consecutive primes)
= (3 x 5) + (3 + 5)
= 3 x 2^{3} + (1)^{3} (sum of 4
cubes)
= 2 x 2^{3} + 7 x 1^{3} (sum of
9 positive cubes)
= 12^{2}  11^{2}
=  (2^{2}  3^{3})
= 1^{4} + 2^{3} + 3^{2} + 4^{1} +
5^{0}
10^{23} 
23 = 99,999,999,999,999,999,999,977 is the largest 23 digit prime.
23 x
2239 x 2393
= 123232321 (palindromic
prime)
Repeat
the digit 1, 23 times like this: 11,111,111,111,111,111,111,111
and you obtain a prime number.
23.140692632779269005...
is e^{π}, also known as the Gelfond's
constant.
The
'Birthday Paradox' states that a group of 23 randomlyselected
persons is the lowest number where there will be a probability
higher than 50 per cent that two people will share the same birthday.
For 60 or more people, the probability is greater than 99 per
cent!
In
telegraphers code 23 means "break the line".
Each
parent contributes 23 chromosomes to the start of human life.
The nuclei of cells in human bodies have 46 chromosomes made
out of 23 pairs.
Twentythree
is the Sacred Number (along with 5) of Eris,
goddess of discord, according to the Principia Discordia;
it is the number of the 'Illuminati'.
Twentythree
is one of the most commonly cited prime numbers... Numerous people
have claimed to see 23's everywhere (the '23 curse') prior to
enormous success and fruitfulness. 23rdians are
a group of persons who subscribe to the mystical power of 23
and see it in multiple combinations throughout daily life.
The
23rd letter of the alphabet is 'W'. Therefore, white supremacists and
racist skinheads use 23 in tattoos to represent
'W', as an abbreviation for the word "white".
The Earth
is tilted at an angle of 23.44 degrees
(at the moment!).
Buy
your favorite
Number (23) here.

06  712  1323  2469  70200  201684  5H0P
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1. We always credit our sources, when we can.
2. Some of the material on this web section is submitted by our
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Encyclopedia
of Numbers © G. Sarcone, Archimedes Lab,
Genoa, Italy

