There are 7 letters in TUESDAY, which is the only day of the week whose name contains a prime number of letters. [Gupta]
The first prime number of the form 6n + 1. All primes greater than three have either the form 6n + 1 or 6n - 1.
Graph theorists have been able to prove that 7 colors are required on a donut-shaped map (i.e., an ordinary one-holed torus) to ensure that no adjacent areas are the same.
The first 7 digits of 89 form a prime. [Kulsha]
The only single digit prime number to yield a square when its cube and the cube's proper divisors are added. Thus 73 + (1 + 7 + 72) = 202.
7! - 6! + 5! - 4! + 3! - 2! + 1! is prime. [Guy]
Seven is the only odd prime that becomes "even" by deleting a letter. [Beedassy]
There are only 7 smoothly undulating nine-digit palindromic primes.
"Seventh heaven" is the farthest of the concentric spheres
containing the stars in the Muslim and Cabalist systems.
Pill bugs ("roly-polies") have 7 pairs of legs.
In 1992, Bayer and Diaconis showed that after 7 random riffle shuffles of a deck of 52 cards, every configuration is nearly equally likely.
The Seven Bridges of Königsberg is a famous solved mathematics problem inspired by an actual place (now Kaliningrad, Russia) and situation. [Millington]
The smallest odd full-period prime.
If you turn a U.S. one-dollar bill upside down and place your
thumb over the eagle's head, the shield becomes the Menorah, or the 7 candlesticks of Israel.
Jesus uses the word seven a "perfect number" of times in the last verse of the first chapter in the Book of Revelation. This makes perfect sense because seven is the number of perfection in the Bible. [Zirkle]
The only odd prime that solves 6y2 = (x + 1)(x2 - x + 6). [Ljunggren]
The first prime happy number. Replace a number by the sum of the squares of its digits, and repeat the process until the number equals 1, or it loops endlessly in a cycle which does not include 1. Those numbers for which this process ends in 1 are called happy numbers. There are exactly 7 prime happy numbers less than 100. Can you find all 7?
There are 7 indeterminate forms involving 0, 1, and infinity.
7 Up (or Seven Up) is a brand of a lemon-lime flavored soft drink.
17 + 47 + 47 + 57 + 97 + 97 + 27 + 97 = 14459929. [Randle]
Thabit ibn Qurra (circa 850 A.D.) noted that if n>1 and each of p = 3*2^(n-1) - 1, q = 3*2^n - 1, and r =(p+1)*(q+1) - 1 is prime, then (2^n*p*q) and (2^n*r) are amicable pairs. Descartes wrote to Mersenne in 1638 with the pair 9363584 and 9437056 (n = 7).
Add 7 to 720(10049 - 1)/99 to get a 99-digit undulating prime. [Pickover]
The largest known number of consecutive primes that can be partitioned
into two sets such that the difference of their product is unity:
(5 * 11 * 13) - (2 * 3 * 7 * 17) = 1.
The Clay Mathematics Institute announced in May 2000 a prize of $1,000,000 for each of the 7 unsolved Millennium Prize Problems. The Poincaré conjecture (essentially the first deep conjecture ever made in topology) has been the only Millennium problem solved thus far.
If asked to quickly pick a number between 12 and 5, most people will choose 7.
If n is composite, the first 7 primes of the form sigma(n)/d(n) are Mersenne prime exponents.
Michael Bell proved that 10^(100*n) + n is prime, where n = 7. As of May 2000,
it is the only known prime of this form.
7! + 1919 is a prime number with 19's on both ends. [Kulsha]
There are 7 different notes in a standard major scale in music as well as in a standard minor scale. [Obeidin]
All primes p greater than or equal to 7 divide a concatenation of (p-1) ones. [Murthy]
Using A = 1, B = 2, ..., Z = 26, the sum of all the letter values in the word names of the numbers from 1 to 7 is a prime (367). If 0 is included, the sum is yet another prime (431). [Trotter]
Double 7! to get the exact number of minutes in a week (7 days). [Luhn]
The 'Tractatus Logico-Philosophicus' of Ludwig Wittgenstein brings 7 groups of aphorisms. The 7th group brings only one (a very curious one):
Wovon man nicht sprechen kann, darüber muss man schweigen.
About what one cannot speak, one must keep silent. [Gevisier]
A Mersenne prime (2p - 1) with exponent p = 3. The key prime factor of the perfect number 28. There are 28 3-digit numbers with digits summing to 7 (e.g., 601; 412) among which exactly 7 (e.g., 241; 313) are prime and also among which one (511) is of the form 2q - 1 where q = 3 x 3. The seven 3-digit primes sum to 2281, a prime with an embedded "28" and with first and last digits summing to 3. Note that the number 2281 is also the exponent of the 17th Mersenne prime.
The reversal of (7 - 1)! + 1 is 27 - 1 (a Mersenne prime). [Luhn]
There are "7 deadly sins" used in early Christian teachings to educate and protect followers from basic human instincts (pride, envy, gluttony, lust, anger, avarice, and sloth). [Croll]
The first number of every sextuplet ends with 7. [Luhn]
The sum of the digits of each of the first two multidigit squares is 7. [Sladcik]
The smallest prime of all integers n such that Mordell's equation y^2 = x^3 + n has no integral solutions. [Post]
There were 7 rings of power for the Dwarf-lords in the stories of J.R.R. Tolkien. [Oldenbeuving]
The number of points and lines on the minimal finite projective (or Fano) plane. [Poo Sung]
It is possible to place 7 cigarettes in such a way that each touches the others if the length divided by the diameter of each is greater than or equal to 7*sqrt(3)/2. [Gardner]
7! + 17^2 = 73^2, 7! + 43^2 = 83^2, and 7! + 131^2 = 149^2. All numbers are prime in these 3 solutions to the generalized Brocard's problem. [Krug]
De Morgan suspected Shanks's calculation of  up to 707 digits was wrong because of the lack of 7s contrary to other digits. [Poo Sung]
(77 + 777)/(7 + 7) = 61 is prime. Note that seven 7's are used and 6 + 1 = 7. [Poo Sung]
There were 7 papers in the first edition of the Ramanujan Journal. [Croll]
There are 7 seals in the New Testament's Book of Revelation. [Croll]
There is a persistent rumor that the philosopher G.W.F. Hegel (1770-1831) provided a logical proof within his doctoral dissertation that there could only be 7 planets in the solar system. [Poo Sung]
The only prime whose sum of divisors (p+1) is a cube. [Gupta]
The smallest prime which can be expressed as the sum of a prime and a composite number (7 = 3 + 4). [Murthy]
In most Hindu marriages the bride follows the groom 7 times around the holy fire, which is called a Saptapadi. [Das]
The smallest example of x-y,xx-y,xxx-y all being prime is with digits x=7 and y=4. So 7-4=3, 77-4=73, 777-4=773 are all primes. It is the only solution because one of three consecutive numbers x..x-y is divisible by 3. [Luhn]
(2^7-1)/(2-1) and (2^7+1)/(2+1) are both primes. [Dobb]
Uranus' moon Miranda (as viewed from space) has a "7" embedded in the middle of a rectangular corona that appears to have been formed by viscous icy lavas. Uranus is the 7th planet from the Sun.
There are 7 primes less than 77 that have at least one digit being 7 (7, 17, 37, 47, 67, 71, 73). [Bush]
7 is the smallest integer that is not the difference of two primes. [North]
The very first Menorah for the Tabernacle as commanded by God to be built in the book of Exodus had 7 lamps in it. [Obeidin]
The only prime such that all the positive values of 7-2^k are all primes. [Russo]
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| Seven Segment Display |
Early electronic instruments incorporated alphanumeric displays that employed discrete circuit components known as 7-segment light-emitting diodes (LED's). [McAlee]
The smallest Woodall prime. [Russo]
The smallest cuban prime. The name has nothing to do with Cuba the country.
The bluntnose sevengill shark has 7 long gill slits in front of each pectoral fin. [Jolly]
7 = sod(sod(sod(4444^4444))), where sod(n) is the sum of digits of integer n. [Daly]
The Japanese word "Subaru" refers to an open star cluster called the Seven Sisters (Pleiades).
Kwanzaa (or Kwaanza) is a 7-day festival (December 26 to January 1) celebrated primarily in the United States, honoring African-American heritage. [Karenga]
The number of stars that form the asterism known as the Big Dipper in North America.
Roma was built over 7 hills. [Franco]
The only prime that can be the digital root (sum of digits computed recursively until one digit remains) of a perfect square. [Rupinski]
13 + 17 + 19 = 7^2. [La Haye]
Andrew Wiles spent 7 years working on his solution of Fermat's Last Theorem. [Croll]
7 is the only prime defined as a cube minus one. [Gallardo]
In "Western" music's 12-tone scale, ratios of fractions between 2 and 1 with a one-digit denominator that involve 7 are not used. This is true whether 7 is either in the numerator or denominator. Ratios such as 7/4, 7/5, 7/6, 8/7, 9/7, etc. are often common notes in the music of other cultures or blues music, but not the "Western" equal temperament scale. [Obeidin]
The maximum number of eclipses of the Sun and Moon that can occur in any one year. [Byrd]
7 is the number of frieze groups, i.e., the groups consisting of symmetries of the plane whose group of translations is isomorphic to the group of integers.
In 1995, Ramaré showed that all integers greater than one are the sum of at most 7 prime numbers.
The number of distinct prime knots containing 7 crossings. [Tait]
72 can be written as a sum of squares in 72 + 72 ways. [Hartley]
The smallest sexy prime triplet that is not part of a sexy prime quadruplet or quintuplet starts at 7. I.e, 7+6 and 7+6+6 are also prime. [Opao]
7^12 reversed is prime. [Patterson]
The numbers on opposite sides of a standard die always add up to 7.
The number of rank and good ears of corn that came up upon one stalk in Pharaoh's second dream (Genesis 41:5).
The sum of seven consecutive primes beginning with 7 is seven times the seventh prime. [Post]
The number of visible colors formed by light across a prism. [Gallardo]
According to the History Channel - 7 machine tools started the modern age: Lathe, Planer, Mill, Grinder, Drill, Band Saw, and Punch-Press. [McAlee]
The first exotic differentiable structure was a 7-dimensional hypersphere. It was found by Milnor (1956) using the calculus of octonions. [Poo Sung]
1!*2!*3!*4!*5!*6!*7! + 1 are twin primes. [Gupta]
Atop the Statue of Liberty there are seven spikes, representing the seven seas. [Patterson]
7 of the major planets in our solar system have natural satellites. [Wolfe]
7 is the smallest prime number that is equal to the product
minus the sum of twin primes, i.e., 3*5 - (3+5) = 7. [Teofilatto]
7 is the smallest Carol prime. [McAlee]
7 = 2^5 - 5^2. [Astle]
7 is the only number n such that n = (n)! - prime(n). [Firoozbakht]
Levy's conjecture (1963) states that all odd numbers greater than or equal to 7 are the sum of a prime plus twice a prime. It was named after Hyman Levy, who was apparently unaware that the conjecture was first stated by Émile Lemoine in 1894. [Capelle]
7 is a double Mersenne prime. [Post]
7 is the first centered hexagonal prime. [Post]
The smallest prime followed by a prime number of consecutive composite numbers. [Silva]
7 is the smallest number that cannot be represented as a sum of 3 squares. [Poo Sung]
Assuming Goldbach's conjecture, there is no positive
number that can be written as the sum of exactly 7
primes in exactly 7 ways. [Hartley]
Have you ever noticed that the word "indivisibilities" contains 7 i's?
The smallest prime whose reciprocal has semiprime period length. [Post]
Whilst every Fibonacci number with odd prime subscript is prime, 7 is the first prime not appearing in the Fibonacci sequence. [Beedassy]
John Elway, one of the most formidable figures in NFL
history, wore number 7 for the Denver Broncos.
The smallest prime NSW number. [Beedassy]
There are exactly 7 possible basic shapes for six-sided polyhedra (convex hexahedra). [Caldwell]
7 is the only prime in which a/b + c/d + e/f = a/b * c/d *
e/f, where the variables a through f represent any non-zero
single-digit numbers. [Morse]
The smallest hyperfibonacci prime that is not a Fibonacci
prime. [Post]
Sir Frederick Pollock
conjectured in 1850 that every number is the sum of at
most 7 octahedral
numbers. [Beedassy]
Ladybugs have 7 spots on their back. [McCranie]
Divisibility test for 7 (or 13): Combine the digits in
order into groups of 3 (starting from the right) by
alternating them with positive and negative signs. If the
result is divisible by 7 (or 13 respectively), then so is
the original number. For example, 7 divides 62540982
because 7 divides +(62)-(540)+(982).
The smallest prime p that yields a number of the form pp
when multiplied by the next prime. [Capelle]
Insert 7 in the middle of the 7th power of 7 and you will get a 7-digit prime. [Silva]
7*6*5*4*3*2*1 + 7654321 is a 7-digit prime with first digit 7
and 1*2*3*4*5*6*7 + 1234567 is a 7-digit prime with last
digit 7. [Silva]
The only prime p such that
(p2) <
((p))2. [Capelle]
Patterson's Conjecture: If Pn is the nth prime, then the
series (P1-1 + P2-2 + P3-3 + ... + Pn-n) is divisible by Pn if and only if Pn = 7.
It is possible to
construct
an angle of /7 using 7 matchsticks. [Beedassy]
Although baseball's first World Series, in 1903, was an 8
game series, as was 1912, 1919, and 1921, it has ever since
been a best-of-seven-game series. [Post]
The dimensions of irreducible modules of the exceptional
Lie group G_2 are all congruent to {-1,0,+1} mod 7. A
similar phenomenon occurs for all exceptional Lie groups
and for some classical ones as well. [Rupinski]
The smallest prime subscript n such that
pn+1 is the first prime dividing
#pn+1, (pn being the
nth prime ). [Beedassy]
The only prime equal to the difference of the product and
the sum of the two previous primes. [Silva]
The normal human head bears 7 sense organ openings: 2 eye sockets, 2 ear canals, 2 nostrils, and a mouth. [Beedassy]
The only prime that is member of two pairs of cousin
primes. [Silva]
The 7 heavenly virtues are prudence, temperance, justice,
fortitude, charity, hope and faith. [Croll]
The game Tetris uses 7 one-sided tetrominoes (referred to as I, J, L, O, S, T, and Z). [Poo Sung]
The largest known prime p such that p! + 1
is the square of a prime. [Beedassy]
7 = 98532/14076 is the unique pandigital fraction
expression including 0. [Poo Sung]
The only odd prime p whose n-th power
pn, for any nonzero n below
p, has exactly n digits. [Beedassy]
The checksum of the checksum of the first 7 decimal places
of the common logarithm of 7 is 7 (log 7 = 0.8450980,
8+4+5+0+9+8+0=34, = 3+4). [Vastvision]
There are 72 natural numbers n
such that n is equal to the number of 7's in the decimal
digits of all numbers smaller or equal to n. [Capelle]
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