- Proth number
-
A number of the form k2 + 1, where k is odd, n is a positive integer, and 2 > k.
Wikipedia foundation.
Proth number
Look at other dictionaries:
Proth number — 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 2 n > k . Proth numbers are named after the mathematician François Proth.If a Proth number is prime, it is called Proth prime: Proth … Wikipedia
Proth's theorem — In mathematics, Proth s theorem in number theory is a primality test for Proth numbers. It states that if p is a Proth number, of the form k 2 n + 1 with k odd and k < 2 n , then if for some integer a ,:a^{(p 1)/2}equiv 1 pmod{p},!then p is prime … Wikipedia
Prime number — Prime redirects here. For other uses, see Prime (disambiguation). A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is… … Wikipedia
François Proth — (1852 1879) was a French self taught mathematician farmer who lived near Verdun, France. He stated four primality related theorems, the most famous of which is Proth s theorem, published around 1878. Proth numbers, related to the above mentioned… … Wikipedia
Sierpinski number — In number theory, a Sierpinski number is an odd natural number k such that integers of the form k 2 n + 1 are composite (i.e. not prime) for all natural numbers n .In other words, when k is a Sierpinski number, all members of the following set… … Wikipedia
Fermat number — In mathematics, a Fermat number, named after Pierre de Fermat who first studied them, is a positive integer of the form:F {n} = 2^{2^{ overset{n} {} + 1where n is a nonnegative integer. The first nine Fermat numbers are OEIS|id=A000215:As of|2008 … Wikipedia
1000 (number) — List of numbers Integers ← 1k 2k 3k 4k 5k 6k 7k 8k 9k → Cardinal 1000 one thousand … Wikipedia
2000 (number) — 2000 (two thousand) is the natural number following 1999 and preceding 2001.See also: millennium, year 2000 AD, Y2K, 2000 (disambiguation).Two thousand is the highest number expressible using only two unmodified characters in roman numerals… … Wikipedia
3000 (number) — 3000 (three thousand) is the natural number following 2999 and preceding 3001. It is the smallest number requiring thirteen letters in English (when and is required from 101 forward). In other fields In the novel The Brothers Karamazov by Fyodor… … Wikipedia
600 (number) — For the year 600, see 600 BC or 600 AD. ← 599 601 → 600 List of numbers Integers ← … Wikipedia
