No clean formula exists for generating prime numbers. Prime sieves are used in most prime number algorithms. Primality testing differs from prime number generation
Prime numbers are natural numbers that cannot be divided by any other numbers. Example: 13 is prime because it cannot be divided by 1 or any other numbers
31 is the 11th prime number and a superprime. It is the third Mersenne prime of the form 2n-1. Only two numbers have sum-of-divisors equal to 31: 16 and 25. 31 is the first prime centered pentagonal number
73 is the 21st prime number and emirp with 37. It is the smallest prime congruent to 1 modulo 24. It is the smallest factor of the first composite generalized Fermat number. It is the fourth star number
Palindromic numbers remain unchanged when their digits are reversed. Zero is palindromic by definition in any base. Palindromicity can be applied to natural numbers in any numeral system
The largest known prime number is 2136,279,841-1 with 41,024,320 decimal digits. Found by Luke Durant on October 12, 2024, using cloud-based virtual machine. First and last 120 digits: 881694327503833265553939100378117358971207354509066041067156376412422630694756841441725990347723283108837509739959776874