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" = 10⁹⁹⁹ + "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 OEIS|id=A074282 [Sequence OEIS2C|id=A074282 in OEIS (retrieved 2008-03-06) incorrectly lists 19441 instead of 19411. 10⁹⁹⁹+19411 is prime while 10⁹⁹⁹+19441 is divisible by 197.]

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. [ [http://primes.utm.edu/notes/by_year.html The Largest Known Prime by Year: A Brief History] from the Prime Pages, at the University of Tennessee at Martin]

ee also

* Gigantic prime
* Megaprime

References

External links

* Chris Caldwell, [http://primes.utm.edu/largest.html "The Largest Known Primes"] at The Prime Pages.
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