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This includes the largest known prime 2 ... are primes ending in the decimal digit d. 2n+1: ... Prime gap – Difference between two successive prime numbers;
a Proth prime and a Pierpont prime as it is 3 × 2 5 + 1. [1] the eleventh member of the Mian–Chowla sequence. [2] a self number in base 10, since there is no integer that added to its own digits, adds up to 97. [3] the smallest odd prime that is not a cluster prime. [4] the highest two-digit number where the sum of its digits is a square.
The table below lists the largest currently known prime numbers and probable primes (PRPs) as tracked by the PrimePages and by Henri & Renaud Lifchitz's PRP Records. Numbers with more than 2,000,000 digits are shown.
In 1811, Peter Barlow, not anticipating future interest in perfect numbers, wrote (in An Elementary Investigation of the Theory of Numbers): Euler ascertained that 2 31 − 1 = 2147483647 is a prime number; and this is the greatest at present known to be such, and, consequently, the last of the above perfect numbers [i.e., 2 30 (2 31 − 1 ...
The following table lists the progression of the largest known prime number in ascending order. [4] Here M p = 2 p − 1 is the Mersenne number with exponent p, where p is a prime number. The longest record-holder known was M 19 = 524,287, which was the largest known prime for 144 years. No records are known prior to 1456.
Mersenne primes and perfect numbers are two deeply interlinked types of natural numbers in number theory. Mersenne primes, named after the friar Marin Mersenne, are prime numbers that can be expressed as 2 p − 1 for some positive integer p. For example, 3 is a Mersenne prime as it is a prime number and is expressible as 2 2 − 1.
That is, it is a prime number of the form M n = 2 n − 1 for some integer n. They are named after Marin Mersenne, a French Minim friar, who studied them in the early 17th century. If n is a composite number then so is 2 n − 1. Therefore, an equivalent definition of the Mersenne primes is that they are the prime numbers of the form M p = 2 p ...
A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.