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The number of perfect numbers less than n is less than , where c > 0 is a constant. [53] In fact it is (), using little-o notation. [54] Every even perfect number ends in 6 or 28, base ten; and, with the only exception of 6, ends in 1 in base 9.
So, 6 is a perfect number because the proper divisors of 6 are 1, 2, and 3, and 1 + 2 + 3 = 6. [2] [4] There is a one-to-one correspondence between the Mersenne primes and the even perfect numbers, but it is unknown whether there exist odd perfect numbers. This is due to the Euclid–Euler theorem, partially proved by Euclid and completed by ...
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.
The number of wheels on a Lockheed C-5 Galaxy. In the code for international direct dial phone calls, +28 is unassigned. 028 is the ISO 3166-1 numeric three-digit country code for Antigua and Barbuda. The number of days in the shortest month of the Gregorian calendar, February in common years. All twelve months of the Gregorian calendar have at ...
A semiperfect number that is not divisible by any smaller semiperfect number is called primitive. Every number of the form 2 m p for a natural number m and an odd prime number p such that p < 2 m+1 is also semiperfect. In particular, every number of the form 2 m (2 m+1 − 1) is semiperfect, and indeed perfect if 2 m+1 − 1 is a Mersenne prime.
Every perfect number is also -perfect. [1] However, there are numbers such as 24 which are -perfect but not perfect. The only known -perfect number with three distinct prime factors is 126 = 2 · 3 2 · 7. [2] Every number of form 2^(n - 1) * (2^n - 1) * (2^n)^m where m >= 0, where 2^n - 1 is Prime, are Granville Numbers.
Furthermore, 114,055,847 is the largest exponent below which all other prime exponents have been tested at least once, so all Mersenne numbers below the 51st (M 82589933) have been tested. [34] ^ ‡ The number M 136279841 has 41,024,320 decimal digits. To help visualize the size of this number, if it were to be saved to disk, the resulting ...
A semiperfect number, since 56 is twice a perfect number. A partition number – the number of distinct ways 11 can be represented as the sum of natural numbers. An Erdős–Woods number, since it is possible to find sequences of 56 consecutive integers such that each inner member shares a factor with either the first or the last member. [5]