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PrimePages. The PrimePages is a website about prime numbers originally created by Chris Caldwell at the University of Tennessee at Martin [ 2] who maintained it from 1994 to 2023. 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.
The 5000 largest known primes at The PrimePages The 10,000 largest known probable primes at primenumbers.net PrimeGrid’s 321 Prime Search , about the discovery of 3×2 6090515 −1
A cluster prime is a prime p such that every even natural number k ≤ p − 3 is the difference of two primes not exceeding p. 3, 5, 7, 11, 13, 17, 19, 23, ... (OEIS: A038134) All odd primes between 3 and 89, inclusive, are cluster primes. The first 10 primes that are not cluster primes are: 2, 97, 127, 149, 191, 211, 223, 227, 229, 251.
A prime with one million digits was found in 1999, earning the discoverer a US$50,000 prize. [10] In 2008, a ten-million-digit prime won a US$100,000 prize and a Cooperative Computing Award from the EFF. [9] Time called this prime the 29th top invention of 2008. [11]
The following is a list of all currently known Mersenne primes and perfect numbers, along with their corresponding exponents p. As of 2023, there are 51 known Mersenne primes (and therefore perfect numbers), the largest 17 of which have been discovered by the distributed computing project Great Internet Mersenne Prime Search, or GIMPS. [2]
Amazon Prime Video, or simply Prime Video, is an American subscription video on-demand over-the-top streaming and rental service of Amazon offered both as a stand-alone service and as part of Amazon's Prime subscription. The service primarily distributes films and television series produced or co-produced by Amazon MGM Studios or licensed to ...
Amazon Prime Video is a global on-demand Internet streaming media provider, owned and operated by Amazon, that distributes a number of original programs that includes original series, specials, miniseries, documentaries, and films.
Riemann's prime-power counting function is usually denoted as Π 0 (x) or J 0 (x). It has jumps of 1 / n at prime powers p n and it takes a value halfway between the two sides at the discontinuities of π(x). That added detail is used because the function may then be defined by an inverse Mellin transform. Formally, we may define Π 0 ...