Twin Primes and Sophie Germain’s Prime Numbers
نویسندگان
چکیده
منابع مشابه
Largest known twin primes and Sophie Germain primes
The numbers 242206083 · 238880 ± 1 are twin primes. The number p = 2375063906985 · 219380 − 1 is a Sophie Germain prime, i.e. p and 2p + 1 are both primes. For p = 4610194180515 · 25056 − 1, the numbers p, p + 2 and 2p + 1 are all primes. In the first days of October, 1995, Harvey Dubner [4] found the largest known twin primes with 5129 decimal digits. (Our earlier twin prime record was 6970538...
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with C0 = 1. Their appearances occur in a dazzling variety of combinatorial settings where they are used to enumerate all manner of geometric and algebraic objects (see Richard Stanley’s collection [28, Chap. 6]; an online Addendum is continuously updated). Quite a lot is known about the divisibility of the Catalan numbers; see [2, 10]. They are obviously closely related to the middle binomial ...
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If P is a prime and 2P+1 is also prime, then P is a Sophie Germain prime. In this article several new Sophie Germain primes are reported, which are the largest known at this time. The search method and the expected search times are discussed.
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ژورنال
عنوان ژورنال: The Bulletin of Society for Mathematical Services and Standards
سال: 2013
ISSN: 2277-8020
DOI: 10.18052/www.scipress.com/bsmass.6.1