107
(another Prime Pages' Curiosity)
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+ When Lehmer's polynomial, n2 - 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.

+ 2107 reversed and 2107 - 1 are primes. [Nash]

+ 2107 - 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]

+ 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.

+ The smallest emirp that remains an emirp when sandwiched between two 1's. [Beedassy]

+ 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]




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