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In number theory, a Proth number is a number of the form Number theory is the branch of pure mathematics concerned with the properties of numbers in general, and integers in particular, as well as the wider classes of problems that arise from their study. ...
 where k is odd, n is a positive integer, and 2n>k. Proth numbers are named after the mathematician François Proth. In mathematics, any integer (whole number) is either even or odd. ...
The integers are commonly denoted by the above symbol. ...
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. In mathematics, a prime number (or a prime) is a natural number that has exactly two (distinct) natural number divisors, which are 1 and the prime number itself. ...
Proths theorem states that if p is a prime Proth number ( of the form k * 2^n + 1 with k odd and k < 2^n ), then for some integer a, Where q = ( ( p-1)/2) This means that if you can find some number a, that multiplied it by...
Examples The first Proth numbers are (sequence A080075 in OEIS): The On-Line Encyclopedia of Integer Sequences (OEIS) is an extensive searchable database of integer sequences, freely available on the Web. ...
- 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
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