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A prime gap is the difference between two successive prime numbers. The n -th prime gap, denoted gn or g ( pn) is the difference between the ( n + 1)-st and the n -th prime numbers, i.e. We have g1 = 1, g2 = g3 = 2, and g4 = 4. The sequence ( gn) of prime gaps has been extensively studied; however, many questions and conjectures remain ...
All prime numbers from 31 to 5,131,135,981 for free download. Lists of Primes at the Prime Pages. The Nth Prime Page Nth prime through n=10^12, pi(x) through x=3*10^13, Random prime in same range. Prime Numbers List Full list for prime numbers below 10,000,000,000, partial list for up to 400 digits.
Cramér's conjecture. In number theory, Cramér's conjecture, formulated by the Swedish mathematician Harald Cramér in 1936, [1] is an estimate for the size of gaps between consecutive prime numbers: intuitively, that gaps between consecutive primes are always small, and the conjecture quantifies asymptotically just how small they must be.
The largest known prime number is 2 82,589,933 − 1, 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. [1] A 2020 plot of the number of digits in the largest known prime by year, since the electronic computer.
Green–Tao theorem. In number theory, the Green–Tao theorem, proved by Ben Green and Terence Tao in 2004, states that the sequence of prime numbers contains arbitrarily long arithmetic progressions. In other words, for every natural number k, there exist arithmetic progressions of primes with k terms. The proof is an extension of Szemerédi ...
Legendre's conjecture, proposed by Adrien-Marie Legendre, states that there is a prime number between and for every positive integer . The conjecture is one of Landau's problems (1912) on prime numbers, and is one of many open problems on the spacing of prime numbers. Unsolved problem in mathematics: Does there always exist at least one prime ...
The future for USA Basketball looks bright with A’ja Wilson and Breanna Stewart in their prime. Then there also is a extremely talented young group of players who say they want to be in the pipeline, led by Caitlin Clark, Angel Reese, Paige Bueckers and Juju Watkins.
9780198788287. Closing the Gap: The Quest to Understand Prime Numbers is a book on prime numbers and prime gaps by Vicky Neale, published in 2017 by the Oxford University Press ( ISBN 9780198788287 ). The Basic Library List Committee of the Mathematical Association of America has suggested that it be included in undergraduate mathematics libraries.