65
This number is a composite.
The first 65 digits of 6565 form a prime number. [Honaker]
The product of the first two primes of the form 4n + 1.
Euler found 65 integers, which he called "numeri idonei," that could
be used to prove the primality of certain numbers. [Brown]
665 - 5 is the smallest prime of the form ac - b, where
b = a - 1. Note that c is the concatenation of a and b. [Kulsha]
The smallest composite number of the form n2 + 1, where n is even.
65 is the ONLY number which gives a prime square by adding as well as subtracting its reversal from it: 65 + 56 = 112, 65 - 56 = 32. [Gupta]
The only number which is the difference of fourth powers of two primes. [Murthy]
(65!)2 + 1 is prime. [Dobb]
65 = 5 * 13 and π(65) = π(5) * π(13) = 5 + 13. [Honaker]
The smallest Fermat semiprime. [Capelle]
π(65) = phi(65) - 6*5. [Langroudi]
The smallest square-free semiprime whose ternary representation (2102) is also semiprime when read in decimal. [Bajpai]
The reversal of 65^56 is prime. You can copy and paste RevDigits(65^RevDigits(65,10),10) into the 'Value space' at Alpertron (integer factorization calculator) then click on the 'Prime box' to display this 102-digit number. Can you find a larger prime of this form? [Honaker]