# 20

This number is a composite. The smallest composite number r such that n = 4r + 3 and m = 8r + 7 are primes. [Rivera] Oliver Sacks' describes in his book 'The MAN Who MISTOOK HIS WIFE for a HAT,' a pair of autistic twin brothers who were swapping 20-figure primes. The smallest number n such that neither 6n-1 nor 6n+1 are primes. [Necula] 20 ones plus 20 is prime. This is the largest such two-digit number. [Opao] There are 20 books in the Bible that have a prime number of chapters. [Opao] Reversal(1^20 + 2^20 + ... + 20^20) is prime. Reversal(20) is the only other known number with this property. [Firoozbakht] 20^20 - 11...1 (20 ones) and 20 + 11...1 (20 ones) are primes. [Firoozbakht] The 20th palindromic prime contains a digit sum of 20. [Post] The smallest composite number which, summed to all previous primes, yields a prime. [Silva] π(20) = 2^3 + 0^3. It is the smallest number with this property. [Kumar] The smallest number that cannot be either prefixed or followed by one digit to form a prime. [Homewood] The 20th prime divides the sum of the first 20 primes. 20 is the smallest composite with this property. [Hasler] The only number n < 1000, such that subtracting from it each of the first seven powers of 3, then all absolute differences that are obtained, 20-3^0, 20-3^1, …, 20-3^6 are primes, i.e., 19, 17, 11, 7, 61, 223, 709. [Loungrides] The smallest number n such that 1n1, 3n3, 7n7, 9n9 are all prime. [Bajpai] The smallest number n whose sum of digits equals omega(n).

(There are 4 curios for this number that have not yet been approved by an editor.)