12 (another Prime Pages' Curiosity)
 Curios: Curios Search:   Participate: The sum of twin primes (except for the first pair) is divisible by 12. In the 19th century, the Russian mathematician Chebyshev proved that (x) is greater than x/(12 log x). 12! + 34567 is prime. 12 is the smallest composite number whose sum of digits, product of digits and the sum of the sum of digits and product of digits are all prime. [Gevisier] The only number such that n ± 1 , n/2 ± 1 and n/3 ± 1 are all primes. [Murthy] The smallest multi-digit number exactly divisible by the square of a prime. [Russo] The concatenation of n!, (n-1)!, ..., 2!, 1! and 0! is prime for n=12, 6, 4, 3 and 2, but not for n=11, 10, 9, 8, 7, or 5 (nor for 13, 14, 15, ... up to at least 61). Note that 2, 3, 4, 6 and 12 are exactly the non-unit divisors of 12. [Hartley] 212 + 212 + 312 is prime. Note that 2*2*3 = 12. [Honaker] 12 is the largest known even number expressible as the sum of two primes in one way. [Firoozbakht] 12 = (1*2) * (prime(1)*prime(2)). Note that 12 is the only number less than 20000000 with this property. [Firoozbakht] (12) = prime(1!) + prime(2!) [Firoozbakht] 12 is the smallest number n such that n and n! are product of distinct factorials of primes (12 = 2!3! and 12! = 2!3!11!). [Capelle] The smallest composite number ending in a prime digit. [Silva] The concatenation of the difference and the sum of number 12 and the 12th prime is prime (2549). Note that the concatenation of 12 and the 12th prime is an emirp. [Silva] (12) = 11 + 22. [Kumar] For any prime p > 3, (p2 - 1) is divisible by 12. [Fellows] The smallest oblong number that is the sum of 2 successive primes. [Honaker] (There are 7 curios for this number that have not yet been approved by an editor.) Prime Curios! © 2000-2018 (all rights reserved)  privacy statement