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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.
Mersenne primes and perfect numbers are two deeply interlinked types of natural numbers in number theory. Mersenne primes, named after the friar Marin Mersenne, are prime numbers that can be expressed as 2 p − 1 for some positive integer p. For example, 3 is a Mersenne prime as it is a prime number and is expressible as 2 2 − 1.
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself. However, 4 is composite because it is a ...
In number theory, a Williams number base b is a natural number of the form () for integers b ≥ 2 and n ≥ 1. [1] The Williams numbers base 2 are exactly the Mersenne numbers. A Williams prime is a Williams number that is prime. They were considered by Hugh C. Williams. [2]
Are You Smarter Than a 5th Grader?: History — Where the Past Comes to Haunt You . When did the American Revolutionary War begin? Answer: 1775. What war started on April 12, 1861?
Being approximately 1.695 × 10 694127911065419641, this number is far too large for any currently known primality test. It has no prime factor below 1 × 10 36. [2] There are probably no other double Mersenne primes than the four known. [1] [3] Smallest prime factor of (where p is the nth prime) are