Titanic prime
Encyclopedia
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:
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 .
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 prime
s 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
Samuel Yates was a mathematician who first described unique primes in the 1980s. In 1984 he began the list of "Largest Known Primes" and coined the name titanic prime for any prime with 1,000 or more decimal digits...
in the 1980s, denoting a prime number
Prime number
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example 5 is prime, as only 1 and 5 divide it, whereas 6 is composite, since it has the divisors 2...
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:
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 .
Apart from the early n = 7, these values are not far from the expectation based on the prime number theorem
Prime number theorem
In number theory, the prime number theorem describes the asymptotic distribution of the prime numbers. The prime number theorem gives a general description of how the primes are distributed amongst the positive integers....
.
The first discovered titanic primes were the Mersenne prime
Mersenne prime
In mathematics, a Mersenne number, named after Marin Mersenne , is a positive integer that is one less than a power of two: M_p=2^p-1.\,...
s 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.
External links
- Chris Caldwell, The Largest Known Primes at The Prime PagesPrime pagesThe Prime Pages is a website about prime numbers maintained by Chris Caldwell at the University of Tennessee at Martin.The site maintains the list of the "5,000 largest known primes", selected smaller primes of special forms, and many "top twenty" lists for primes of various forms...
.