Search results
Results from the WOW.Com Content Network
A prime number (or prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. By Euclid's theorem , there are an infinite number of prime numbers. Subsets of the prime numbers may be generated with various formulas for primes .
69×2 14977631 – 1 3 December 2021 4,508,719 65 192971×2 14773498 – 1 7 March 2021 4,447,272 66 4×3 9214845 + 1 10 September 2024 4,396,600 67 9145334×3 9145334 + 1 25 December 2023 4,363,441 68 4×5 6181673 – 1 15 July 2022 4,320,805 69 396101×2 14259638 – 1 3 February 2024 4,292,585 70 6962×31 2863120 – 1 29 February 2020 ...
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.
Similarly, when written in the usual decimal system, all prime numbers larger than 5 end in 1, 3, 7, or 9. The numbers that end with other digits are all composite: decimal numbers that end in 0, 2, 4, 6, or 8 are even, and decimal numbers that end in 0 or 5 are divisible by 5. [11]
L(n) = L(n − 1) + L(n − 2) for n ≥ 2, with L(0) = 2 and L(1) = 1. A000032: Prime numbers p n: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, ... The prime numbers p n, with n ≥ 1. A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers. A000040: Partition numbers P n: 1, 1, 2, 3, 5, 7, 11, 15, 22, 30 ...
The first: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23 (sequence A005408 in the OEIS). All integers are either even or odd. All integers are either even or odd. A square has even multiplicity for all prime factors (it is of the form a 2 for some a ).
The largest known prime number is 2 136,279,841 − 1, a number which has 41,024,320 digits when written in the decimal system. It was found on October 12, 2024, on a cloud-based virtual machine volunteered by Luke Durant, a 36-year-old researcher from San Jose, California, to the Great Internet Mersenne Prime Search (GIMPS).
For example, the AP-3 {3, 7, 11} does not qualify, because 5 is also a prime. For an integer k ≥ 3, a CPAP-k is k consecutive primes in arithmetic progression. It is conjectured there are arbitrarily long CPAP's. This would imply infinitely many CPAP-k for all k. The middle prime in a CPAP-3 is called a balanced prime.