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31 is the 11th prime number. It is a superprime and a self prime (after 3, 5, and 7), as no integer added up to its base 10 digits results in 31. [1] It is the third Mersenne prime of the form 2 n − 1, [2] and the eighth Mersenne prime exponent, [3] in-turn yielding the maximum positive value for a 32-bit signed binary integer in computing: 2,147,483,647.
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.
[28] [29] As of September 2022, the Mersenne number M 1277 is the smallest composite Mersenne number with no known factors; it has no prime factors below 2 68, [30] and is very unlikely to have any factors below 10 65 (~2 216). [31] The table below shows factorizations for the first 20 composite Mersenne numbers (sequence A244453 in the OEIS).
All prime numbers from 31 to 6,469,693,189 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 primes in same range. Interface to a list of the first 98 million primes (primes less than 2,000,000,000) Weisstein, Eric W. "Prime Number Sequences". MathWorld.
The same prime factor may occur more than once; this example has two copies of the prime factor When a prime occurs multiple times, exponentiation can be used to group together multiple copies of the same prime number: for example, in the second way of writing the product above, 5 2 {\displaystyle 5^{2}} denotes the square or second power of ...
31: prime: 2147483647 7: 127: prime: ... Since is a Mersenne number, such a prime factor would have to be of the form + . Additionally, because is composite when ...
A Gaussian integer is either the zero, one of the four units (±1, ±i), a Gaussian prime or composite.The article is a table of Gaussian Integers x + iy followed either by an explicit factorization or followed by the label (p) if the integer is a Gaussian prime.
Not all Euclid numbers are prime. E 6 = 13# + 1 = 30031 = 59 × 509 is the first composite Euclid number.. Every Euclid number is congruent to 3 modulo 4 since the primorial of which it is composed is twice the product of only odd primes and thus congruent to 2 modulo 4.