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.

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.

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

See also

• Gigantic prime
• Megaprime

External links

• Chris Caldwell, The Largest Known Primes and "Smallest Titanics of Special Forms" at The Prime Pages.