# 107

When Lehmer's polynomial, *n*^{2} - *n* + 67374467, is evaluated at an integer *n*, the result is never divisible by any prime less than 107. [Kravitz]

The first three-digit Mersenne prime exponent.

2^{107} reversed and 2^{107} - 1 are primes. [Nash]

Maximum duration of a Lunar eclipse is 107 minutes. [Gupta]

2^{107} - 1 is the largest known Mersenne prime not containing all the individual digits. [Luhn]

Allan Brady proved in 1983 that the maximal number of steps that a four-state Turing machine can make on an initially blank tape before eventually halting is 107.

Rudy Giuliani was the 107th mayor of New York City. [Trotter]

There is no integer *N* such that *N*! has exactly 107 zeros in it. The same is true if we replace 107 by the primes 3, 31, or 43. [Sudipta Das]

The Peugeot 107 is a city car produced by the French automaker Peugeot. (It has proved to be quite popular with British buyers.)

Space Shuttle Columbia (STS-107 mission) disintegrated during reentry. [Gupta]

"One hundred and seven" is the smallest positive integer requiring six syllables (in English) if 'and' is included.

Many Lucas numbers are not prime, but "Lucas" is (chemically) prime if we add the atomic numbers of Lu(tetium), Ca(lcium) and S(ulphur): 71 + 20 + 16 = 107. [Necula]

The sum of atomic numbers of five chemical elements that have their symbols embedded in the second author's last name (H,O,Na,K,Er). [Necula]

The smallest twin, cousin, and sexy prime, where all are Cyclops primes. [Punches]

The smallest 3-digit prime which remains prime when 2 is added to any of its digits. I.e., 307, 127, and 109 are primes. [Opao]

107 = 1!_{2} + 0!_{2} + 7!_{2}. Note that the prime number 107 is the largest number with this property. [Firoozbakht]

The smaller of a pair of twin hyperfactorial primes: 107 = (1^1 * 2^2 * 3^3) - 1. [Post]

The smallest prime number which is sum of different primes ending with the digit nine. [Capelle]

There are exactly 107 hole-free heptominoes (polyominoes made up of seven squares connected edge-to-edge). [Beedassy]

107 = 2+3*5*7 = 2*3*5+7*11. [Rivera]

The deity worshipped by the Hindus as Krishna, meaning dark-complexioned Lord, is also known by His other 107 transcendental attributes. [Beedassy]

Each of the 1+0+7 numbers, 107+2!, 107+3!, ..., 107+9!, are prime! [Firoozbakht]

The smallest Cyclops emirp. [Capelle]

If A_n = 1!+3!+5!+...+(2n-1)!, then 107 divides A_53 and so 107 divides all A_n for n>=53. [Marot]

107 Camilla is one of the largest main belt asteroids. It has a very dark surface and primitive carbonaceous composition. [Pogson]

Radio station WEZX ("Rock 107") broadcasts from Scranton, Pennsylvania.

There are 107 possible carrier frequencies for AM radio signals that may be assigned (535-1605 kHz band, at 10 kHz intervals).

The smallest safe prime that is an emirp. [Loungrides]

The first occurrence of two successive twin prime pairs {(107, 109) ; (137, 139)} whose smaller and larger members concatenate respectively into a prime (107137) and an emirp (109139). Note that the reverse concatenation of the larger members also forms an emirp (139109). [Beedassy]

The number of edges in the "continguous USA graph" whose 49 vertices represent the contiguous 48 states of the United States plus the District of Columbia (DC) and whose edges connect pairs states (plus DC) which are connected by at least one drivable road. [Post]

107 is the smallest prime p where pth digit of π is a zero. [Gudipati]

The smallest emirp that does not produce a prime by adding a digit to it. (There is no prime "107d"). [Loungrides]

Hyperpyrexia is an severe elevation of body temperature corresponding to a high grade fever of 107 degrees Fahrenheit or above. [Beedassy]

2^107*107!-1 is the largest non-titanic prime of form 2^p*p!-1 where p is a prime. This says that the product of first 107 positive even numbers minus 1 is prime, i.e., 2*4*6*...*210*212*214-1. [Loungrides]

107 is equal to the sum of the digits of 107^n for n=11, 13 and 15. E.g., 107^11 = 21048519522998348950643 and SOD(21048519522998348950643) = 107. [Rivera]

107 and 109 are the smallest pair of consecutive prime numbers whose squares have the same sum of digits. [Gaydos]

107 is prime in binary if counted as 1 x 4 + 0 x 2 + 7 x 1 = 11. Counting this way it is also prime in bases 4, 6, 8, 10 and 12. [Homewood]

(107, 1439) is the first pair of emirps of form (p-666, p+666), (case p=773), i.e., 773 is a beastly cousins prime. [Loungrides]

2^107-1 is the smallest Mersenne prime that contains the digit sequence equal to the number of its digits, i.e., 33. [Harrison]