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Many properties of a natural number n can be seen or directly computed from the prime factorization of n.. The multiplicity of a prime factor p of n is the largest exponent m for which p m divides n.
The only base-4 repunit prime is 5 (). = (+) (), and 3 always divides + when n is odd and when n is even. For n greater than 2, both + and are greater than 3, so removing the factor of 3 still leaves two factors greater than 1.
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.
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Name First elements Short description OEIS Mersenne prime exponents : 2, 3, 5, 7, 13, 17, 19, 31, 61, 89, ... Primes p such that 2 p − 1 is prime.: A000043 ...
Lucas numbers have L 1 = 1, L 2 = 3, and L n = L n−1 + L n−2. Primefree sequences use the Fibonacci recursion with other starting points to generate sequences in which all numbers are composite. Letting a number be a linear function (other than the sum) of the 2 preceding numbers. The Pell numbers have P n = 2P n−1 + P n−2.
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840 = 2 3 × 3 × 5 × 7, highly composite number, [34] smallest number divisible by the numbers 1 to 8 (lowest common multiple of 1 to 8), sparsely totient number, [35] Harshad number in base 2 through base 10, idoneal number, balanced number, [36] sum of a twin prime (419 + 421).