A megaprime is a
prime number
A prime number (or a prime) is a natural number greater than 1 that is not a 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 because the only ways ...
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 the 1980s. In 1984 he began the list of "Largest Known Primes" (today Th ...
in the 1980s for a prime with at least 1000 digits, and gigantic prime for a prime with at least 10,000 digits. Bevaprime has been proposed for a prime with at least 1,000,000,000 digits.
, there are more than 1500 known megaprimes
[Chris Caldwell]
The Largest Known Primes
at The PrimePages. and 85 further
probable prime
In number theory, a probable prime (PRP) is an integer that satisfies a specific condition that is satisfied by all prime numbers, but which is not satisfied by most composite numbers. Different types of probable primes have different specific con ...
s (PRPs) which have more than 1,000,000 digits.
[Henri Lifchitz & Renaud Lifchitz, Probable Primes Top 10000](_blank)
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 17th ...
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 17 ...
, a participant in the
distributed computing
A distributed system is a system whose components are located on different networked computers, which communicate and coordinate their actions by passing messages to one another from any system. Distributed computing is a field of computer sci ...
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 an ...
.
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 an ...
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 international non-profit digital rights group based in San Francisco, California. The foundation was formed on 10 July 1990 by John Gilmore, John Perry Barlow and Mitch Kapor to promote Internet ci ...
from the
Electronic Frontier Foundation for this achievement.
Almost all 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 10
999999 through 10
999999 + 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 materials
...
, and there is a very high probability that 10
999999 + 593499, a
strong probable prime, is the smallest megaprime.
[Patrick De Geest]
10^999999 + y
World!Of Numbers , the smallest number known to be a megaprime is 10
999999 + 308267*10
292000 + 1.
The last prime that is not a megaprime is almost certainly 10
999999 - 172473.
See also
*
List of largest known primes and probable primes
The table below lists the largest currently known prime numbers and probable primes (PRPs) as tracked by the University of Tennessee's PrimePages and Henri & Renaud Lifchitz' PRP Records. Numbers with more than 2,000,000 digits are shown.
Largest ...
, a list that includes the largest known megaprimes and probable megaprimes
*
Largest known prime number
The largest known prime number () is , a number which has 24,862,048 digits when written in base 10. It was found via a computer volunteered by Patrick Laroche of the Great Internet Mersenne Prime Search (GIMPS) in 2018.
A prime number is a posi ...
*
References
{{Large numbers
Prime numbers
Large integers