Proth number

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In number theory, a Proth number is a number of the form

P=k\, 2^n+1

where k is odd, n is a positive integer, and 2n>k. Proth numbers are named after the mathematician François Proth.

If a Proth number is prime, it is called Proth prime: Proth's theorem can be used to test the primality of a given Proth number.

[edit] Examples

The first Proth numbers are (sequence A080075 in OEIS):

P0 = 21 + 1 = 3
P1 = 22 + 1 = 5
P2 = 23 + 1 = 9
P3 = 3 × 22 + 1 = 13
P4 = 24 + 1 = 17
P5 = 3 × 23 + 1 = 25
P6 = 25 + 1 = 33

The first Proth primes are (A080076):

3, 5, 13, 17, 41, 97, 113, 193, 241, 257, 353, 449, 577, 641, 673, 769, 929, 1153, 1217, 1409, 1601, 2113, 2689, 2753, 3137, 3329, 3457, 4481, 4993, 6529, 7297, 7681, 7937, 9473, 9601, 9857

[edit] See also


[edit] External links

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