MathWorld Headline News

Two Gigantic Primes with Prime Digits Found

By Eric W. Weisstein

April 9, 2002--The search for large prime numbers having various interesting properties remains a challenging computational problem in both cryptography and recreational mathematics. While state-of-the-art algorithms such as the number field sieve and the elliptic curve factorization method are capable of factoring general numbers of up to around 130 digits, probabilistic primality tests can be used to establish the primality or compositeness of much larger numbers, currently up to around 15,000 digits (i.e., far into the range of gigantic primes).

One class of prime numbers of interest to recreational mathematicians is the class of prime numbers whose digits are themselves all prime (i.e., consist of only 2, 3, 5, and 7). This class is one type of Smarandache sequence, which is simply a set of diverse integer sequences chosen for their recreational interest (Smith 1996, Mudge 1997). In February of 2002, H. Dubner found the largest-known members of the sequence of prime numbers all of whose digits are prime,

and

where R_n is a so-called repunit (i.e., a number consisting of n 1's). Both of these numbers have 15,600 digits, making them challenging to have their primality checked even on extremely fast computers.