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This is a list of articles about prime numbers. 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.
For example, among the numbers 1 through 6, the numbers 2, 3, and 5 are the prime numbers, [6] as there are no other numbers that divide them evenly (without a remainder). 1 is not prime, as it is specifically excluded in the definition. 4 = 2 × 2 and 6 = 2 × 3 are both composite.
This property implies that no Euclid number can be a square. For all n ≥ 3 the last digit of E n is 1, since E n − 1 is divisible by 2 and 5. In other words, since all primorial numbers greater than E 2 have 2 and 5 as prime factors, they are divisible by 10, thus all E n ≥ 3 + 1 have a final digit of 1.
When written in base 10, all multiples of 2 will end in 0, 2, 4, 6, or 8. [3] 2 is the smallest and the only even prime number, and the first Ramanujan prime. [4] It is also the first superior highly composite number, [5] and the first colossally abundant number. [6]
A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.
In 1811, Peter Barlow, not anticipating future interest in perfect numbers, wrote (in An Elementary Investigation of the Theory of Numbers): Euler ascertained that 2 31 − 1 = 2147483647 is a prime number; and this is the greatest at present known to be such, and, consequently, the last of the above perfect numbers [i.e., 2 30 (2 31 − 1 ...
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For example, all prime numbers have a prime signature of {1}, the squares of primes have a prime signature of {2}, the products of 2 distinct primes have a prime signature of {1, 1} and the products of a square of a prime and a different prime (e.g. 12, 18, 20, ...) have a prime signature of {2, 1}.