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Twenty-three is also the next to last member of the first Cunningham chain of the first kind (2, 5, 11, 23, 47), [3] and the sum of the prime factors of the second set of consecutive discrete semiprimes, (21, 22). 23 is the smallest odd prime to be a highly cototient number, as the solution to () for the integers 95, 119, 143, and 529.
A prime number (or prime) is a ... Some sources only list the smallest prime in each cycle, ... The primes of the form 2n+1 are the odd primes, ...
A prime number is a natural number that has exactly two distinct natural number divisors: the number 1 and itself. To find all the prime numbers less than or equal to a given integer n by Eratosthenes' method: Create a list of consecutive integers from 2 through n: (2, 3, 4, ..., n). Initially, let p equal 2, the smallest prime number.
127 is the smallest odd number that cannot be written in the form +, for p is a prime number, and x is an integer, since =, =, =, =, =, =, and = are all composite numbers. [ 8 ] 127 is an isolated prime where neither p − 2 {\displaystyle p-2} nor p + 2 {\displaystyle p+2} is prime.
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.
Ω(n), the prime omega function, is the number of prime factors of n counted with multiplicity (so it is the sum of all prime factor multiplicities). A prime number has Ω(n) = 1. The first: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37 (sequence A000040 in the OEIS). There are many special types of prime numbers. A composite number has Ω(n) > 1.
a self number in base 10, since there is no integer that added to its own digits, adds up to 97. [3] the smallest odd prime that is not a cluster prime. [4] the highest two-digit number where the sum of its digits is a square. the number of primes <= 2 9. [5] The numbers 97, 907, 9007, 90007 and 900007 are all primes, and they are all happy primes.
The first, smallest, and only odd prime gap is the gap of size 1 between 2, the only even prime number, and 3, the first odd prime. All other prime gaps are even. There is only one pair of consecutive gaps having length 2: the gaps g 2 and g 3 between the primes 3, 5, and 7.