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A cluster prime is a prime p such that every even natural number k ≤ p − 3 is the difference of two primes not exceeding p. 3, 5, 7, 11, 13, 17, 19, 23, ... (OEIS: A038134) All odd primes between 3 and 89, inclusive, are cluster primes. The first 10 primes that are not cluster primes are: 2, 97, 127, 149, 191, 211, 223, 227, 229, 251.
The same prime factor may occur more than once; this example has two copies of the prime factor When a prime occurs multiple times, exponentiation can be used to group together multiple copies of the same prime number: for example, in the second way of writing the product above, 5 2 {\displaystyle 5^{2}} denotes the square or second power of 5 ...
27 has an aliquot sum of 13 [2] (the sixth prime number) in the aliquot sequence (27, 13, 1, 0) of only one composite number, rooted in the 13-aliquot tree. [ 3 ] In the Collatz conjecture (i.e. the 3 n + 1 {\displaystyle 3n+1} problem), a starting value of 27 requires 3 × 37 = 111 steps to reach 1, more than any smaller number.
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Country codes are defined by the International Telecommunication Union (ITU) in ITU-T standards E.123 and E.164. The prefixes enable international direct dialing (IDD). Country codes constitute the international telephone numbering plan. They are used only when dialing a telephone number in a country or world region other than the caller's.
A variation of the conjecture asserting that x, y, z (instead of A, B, C) must have a common prime factor is not true. A counterexample is + =, in which 4, 3, and 7 have no common prime factor. (In fact, the maximum common prime factor of the exponents that is valid is 2; a common factor greater than 2 would be a counterexample to Fermat's Last ...
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The dominant customary international law standard of statehood is the declarative theory of statehood, which was codified by the Montevideo Convention of 1933. The Convention defines the state as a person of international law if it "possess[es] the following qualifications: (a) a permanent population; (b) a defined territory; (c) government; and (d) a capacity to enter into relations with the ...