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Below are listed the first prime numbers of many named forms and types. More details are in the article for the name. ... where p n is the nth prime. 5, 11, 17, 29, ...
Ω(n), the prime omega function, is the number of prime factors of n counted with multiplicity (so it is the sum of all prime factor multiplicities). A prime number has Ω(n) = 1. The first: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37 (sequence A000040 in the OEIS). There are many special types of prime numbers. A composite number has Ω(n) > 1.
The first 25 prime numbers ... all primes up to the square root of the table size have been processed, and all remaining unmarked numbers (11, 13, etc.) are marked as ...
For example, 3 is a Mersenne prime as it is a prime number and is expressible as 2 2 − 1. [ 1 ] [ 2 ] The exponents p corresponding to Mersenne primes must themselves be prime, although the vast majority of primes p do not lead to Mersenne primes—for example, 2 11 − 1 = 2047 = 23 × 89 .
It is the set of numbers between 1 and the product P i = p 1 · p 2 ⋯ p i of the first i prime numbers that are ... 1 2 3 5 7 11 13 17 19 23 25 29. The first number ...
11 is a prime number, and a super-prime. 11 forms a twin prime with 13, [6] and sexy pair with 5 and 17. 11 is also the first prime exponent that does not yield a Mersenne prime. 11 is also a Gaussian prime [7] and an Eisenstein prime. [8] 11 is part of a pair of Brown numbers. Only three such pairs of numbers are known. [citation needed] Rows ...
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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.