About: Cluster prime

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In number theory, a cluster prime is a prime number p such that every even positive integer k ≤ p − 3 can be written as the difference between two prime numbers not exceeding p. For example, the number 23 is a cluster prime because 23 − 3 = 20, and every even integer from 2 to 20, inclusive, is the difference of at least one pair of prime numbers not exceeding 23: * 5 − 3 = 2 * 7 − 3 = 4 * 11 − 5 = 6 * 11 − 3 = 8 * 13 − 3 = 10 * 17 − 5 = 12 * 17 − 3 = 14 * 19 − 3 = 16 * 23 − 5 = 18 * 23 − 3 = 20 97, 127, 149, 191, 211, 223, 227, 229, ... OEIS: Unsolved problem in mathematics:

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  • In number theory, a cluster prime is a prime number p such that every even positive integer k ≤ p − 3 can be written as the difference between two prime numbers not exceeding p. For example, the number 23 is a cluster prime because 23 − 3 = 20, and every even integer from 2 to 20, inclusive, is the difference of at least one pair of prime numbers not exceeding 23: * 5 − 3 = 2 * 7 − 3 = 4 * 11 − 5 = 6 * 11 − 3 = 8 * 13 − 3 = 10 * 17 − 5 = 12 * 17 − 3 = 14 * 19 − 3 = 16 * 23 − 5 = 18 * 23 − 3 = 20 On the other hand, 149 is not a cluster prime because 140 < 146, and there is no way to write 140 as the difference of two primes that are less than or equal to 149. By convention, 2 is not considered to be a cluster prime. The first 23 odd primes (up to 89) are all cluster primes. The first few odd primes that are not cluster primes are 97, 127, 149, 191, 211, 223, 227, 229, ... OEIS: It is not known if there are infinitely many cluster primes. Unsolved problem in mathematics: Are there infinitely many cluster primes? (more unsolved problems in mathematics) (en)
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  • Cluster Prime (en)
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  • ClusterPrime (en)
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  • In number theory, a cluster prime is a prime number p such that every even positive integer k ≤ p − 3 can be written as the difference between two prime numbers not exceeding p. For example, the number 23 is a cluster prime because 23 − 3 = 20, and every even integer from 2 to 20, inclusive, is the difference of at least one pair of prime numbers not exceeding 23: * 5 − 3 = 2 * 7 − 3 = 4 * 11 − 5 = 6 * 11 − 3 = 8 * 13 − 3 = 10 * 17 − 5 = 12 * 17 − 3 = 14 * 19 − 3 = 16 * 23 − 5 = 18 * 23 − 3 = 20 97, 127, 149, 191, 211, 223, 227, 229, ... OEIS: Unsolved problem in mathematics: (en)
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  • Cluster prime (en)
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