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Therefore, every prime number other than 2 is an odd number, and is called an odd prime. [9] 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 ...
All odd primes between 3 and 89, inclusive, are cluster primes. ... Prime Numbers List Full list for prime numbers below 10,000,000,000, partial list for up to 400 ...
Even and odd numbers: An integer is even if it is a multiple of 2, and is odd otherwise. Prime number: A positive integer with exactly two positive divisors: itself and 1. The primes form an infinite sequence 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, ...
A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.
This works with all perfect numbers () with odd prime p and, in fact, with all numbers of the form () for odd integer (not necessarily prime) m. Owing to their form, 2 p − 1 ( 2 p − 1 ) , {\displaystyle 2^{p-1}(2^{p}-1),} every even perfect number is represented in binary form as p ones followed by p − 1 zeros; for example:
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 first: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144 (sequence A000290 in the OEIS). A cube has all multiplicities divisible by 3 (it is of the form a 3 for some a).
It is also not known if any odd perfect numbers exist; various conditions on possible odd perfect numbers have been proven, including a lower bound of 10 1500. The following is a list of all currently known Mersenne primes and perfect numbers, along with their corresponding exponents p.
A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Equivalently, it is a positive integer that has at least one divisor other than 1 and itself. [1] [2] Every positive integer is composite, prime, or the unit 1, so the composite numbers are exactly the numbers that are not prime and not a ...