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  2. List of Mersenne primes and perfect numbers - Wikipedia

    en.wikipedia.org/wiki/List_of_Mersenne_primes...

    In 1747, Leonhard Euler completed what is now called the Euclid–Euler theorem, showing that these are the only even perfect numbers. As a result, there is a one-to-one correspondence between Mersenne primes and even perfect numbers, so a list of one can be converted into a list of the other. [1] [5] [6]

  3. Perfect number - Wikipedia

    en.wikipedia.org/wiki/Perfect_number

    In number theory, a perfect number is a positive integer that is equal to the sum of its positive proper divisors, that is, divisors excluding the number itself. For instance, 6 has proper divisors 1, 2 and 3, and 1 + 2 + 3 = 6, so 6 is a perfect number. The next perfect number is 28, since 1 + 2 + 4 + 7 + 14 = 28.

  4. Table of prime factors - Wikipedia

    en.wikipedia.org/wiki/Table_of_prime_factors

    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.

  5. Category:Perfect numbers - Wikipedia

    en.wikipedia.org/wiki/Category:Perfect_numbers

    Notably, absent consensus, please do not add articles about individual perfect numbers themselves (such as 6). Pages in category "Perfect numbers" The following 11 pages are in this category, out of 11 total.

  6. Wikipedia:Featured list candidates/List of Mersenne primes ...

    en.wikipedia.org/wiki/Wikipedia:Featured_list...

    Toggle List of Mersenne primes and perfect numbers subsection. 1.1 Comments by RunningTiger123. 1.2 Accessibility review (MOS:DTAB) 1.3 Image review — Pass.

  7. Mersenne prime - Wikipedia

    en.wikipedia.org/wiki/Mersenne_prime

    Mersenne primes M p are closely connected to perfect numbers. In the 4th century BC, Euclid proved that if 2 p − 1 is prime, then 2 p − 1 (2 p − 1) is a perfect number. In the 18th century, Leonhard Euler proved that, conversely, all even perfect numbers have this form. [5] This is known as the Euclid–Euler theorem.

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  9. List of numbers - Wikipedia, the free encyclopedia

    en.wikipedia.org/wiki/List_of_numbers

    A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.