# Titanic prime

Titanic prime is a term coined by Samuel Yates in the 1980s, denoting a prime number of at least 1000 decimal digits. Few such primes were known then, but the required size is trivial for modern computers.[1]

The first 30 titanic primes are of the form:

$p = 10^{999} + n,$

for n one of 7, 663, 2121, 2593, 3561, 4717, 5863, 9459, 11239, 14397, 17289, 18919, 19411, 21667, 25561, 26739, 27759, 28047, 28437, 28989, 35031, 41037, 41409, 41451, 43047, 43269, 43383, 50407, 51043, 52507 (sequence A074282 in OEIS).

Apart from the early n = 7, these values are not far from the expectation based on the prime number theorem.

The first discovered titanic primes were the Mersenne primes 24253−1 with 1281 digits, and 24423−1 with 1332 digits. They were both found November 3, 1961, by Alexander Hurwitz. It is a matter of definition which one was discovered first, since the primality of 24253−1 was computed first, but Hurwitz saw the computer output about 24423−1 first.[2]

Samuel Yates called those who proved the primality of a titanic prime titans.