# 20

This number is a composite.

The smallest composite number *r* such that n = 4*r* + 3 and m = 8*r* + 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]

*e* cubed is close to 20. [Meyes]

In the ninth book of Euclid's work “Elements,” in Proposition 20, there appears for the first time a mathematical proof of the theorem that there are infinitely many prime numbers. [Shalit]

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).