A megaprime is a

prime number A prime number (or a prime) is a natural number greater than 1 that is not a Product (mathematics), product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime ...

with at least one million decimal digits. Other terms for large primes include "titanic prime", coined by

Samuel Yates Samuel Yates (May 10, 1919 in Savannah, Georgia – April 22, 1991 in New Brunswick, New Jersey) was a computer engineer and mathematician who first described unique primes in 1980. In 1984 he began the list of "Largest Known Primes" (today The ...

in the 1980s for a prime with at least 1000 digits (of which the smallest is 10⁹⁹⁹+7), and "gigantic prime" for a prime with at least 10,000 digits (of which the smallest is 10⁹⁹⁹⁹+33603). Megaprimes found by year

, there are 3,354 known megaprimesChris Caldwell
The Largest Known Primes
at The PrimePages. which have more than 1,000,000 digits.Henri Lifchitz & Renaud Lifchitz, Probable Primes Top 10000
primenumbers.net The first to be found was the

Mersenne prime In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form for some integer . They are named after Marin Mersenne, a French Minim friar, who studied them in the early 1 ...

2^6972593−1 with 2,098,960 digits, discovered in 1999 by

Nayan Hajratwala In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form for some integer . They are named after Marin Mersenne, a French Minim friar, who studied them in the early 17t ...

, a participant in the

distributed computing Distributed computing is a field of computer science that studies distributed systems, defined as computer systems whose inter-communicating components are located on different networked computers. The components of a distributed system commu ...

project

GIMPS The Great Internet Mersenne Prime Search (GIMPS) is a collaborative project of volunteers who use freely available software to search for Mersenne prime numbers. GIMPS was founded in 1996 by George Woltman, who also wrote the Prime95 client and ...

press release
''GIMPS Finds First Million-Digit Prime''
Retrieved on 2008-01-04.Chris Caldwell

at The PrimePages. Retrieved on 2008-09-28. Nayan was awarded a

Cooperative Computing Award The Electronic Frontier Foundation (EFF) is an American international non-profit digital rights group based in San Francisco, California. It was founded in 1990 to promote Internet civil liberties. It provides funds for legal defense in court, ...

from the

Electronic Frontier Foundation The Electronic Frontier Foundation (EFF) is an American international non-profit digital rights group based in San Francisco, California. It was founded in 1990 to promote Internet civil liberties. It provides funds for legal defense in court, ...

for this achievement.

Almost all In mathematics, the term "almost all" means "all but a negligible quantity". More precisely, if X is a set (mathematics), set, "almost all elements of X" means "all elements of X but those in a negligible set, negligible subset of X". The meaning o ...

primes are megaprimes, as the number of primes with fewer than one million digits is finite. However, the vast majority of known primes are not megaprimes. All numbers from 10⁹⁹⁹⁹⁹⁹ through 10⁹⁹⁹⁹⁹⁹ + 593498 are known to be

composite Composite or compositing may refer to: Materials * Composite material, a material that is made from several different substances ** Metal matrix composite, composed of metal and other parts ** Cermet, a composite of ceramic and metallic material ...

, and there is a very high probability that 10⁹⁹⁹⁹⁹⁹ + 593499, a strong probable prime for each of 8 different bases, is the smallest megaprime.Patrick De Geest
10^999999 + y
World!Of Numbers , the smallest number known to be a megaprime is 10⁹⁹⁹⁹⁹⁹ + 308267×10²⁹²⁰⁰⁰ + 1. The last prime that is not a megaprime is currently unknown. , the largest prime number known to not be a megaprime is 10⁹⁹⁹⁹⁹⁹ − 1022306×10²⁸⁷⁰⁰⁰ − 1. There is a very high probability that 10⁹⁹⁹⁹⁹⁹ − 172473 is the biggest non-mega prime.

References

{{Large numbers Prime numbers Large integers

See also

References