A prime number p is called a Sophie Germain prime if 2p + 1 is also prime. For example, 23 is a Sophie Germain prime because it is a prime and 2 × 23 + 1 = 47, also prime. These numbers are named after French mathematician Sophie Germain. In mathematics, a prime number (or prime) is a natural number greater than one whose only positive divisors are one and itself. ... This article is in need of attention from an expert on the subject. ... Image:Marie-Sophie Germain. ...

It is conjectured that there are infinitely many Sophie Germain primes, but like the twin prime conjecture, this has not been proven. The first few Sophie Germain primes are (sequence A005384 in OEIS): In mathematics, a conjecture is a mathematical statement which has been proposed as a true statement, but which no one has yet been able to prove or disprove. ... Infinity is a word carrying a number of different meanings in mathematics, philosophy, theology and everyday life. ... The twin prime conjecture is a famous problem in number theory that involves prime numbers. ... In mathematics, a proof is a demonstration that, given certain axioms, some statement of interest is necessarily true. ... The On-Line Encyclopedia of Integer Sequences (OEIS) is a web-based searchable database of integer sequences. ...

2, 3, 5, 11, 23, 29, 41, 53, 83, 89, 113, 131, 173, 179, 191, 233, ...

Currently, the largest known Sophie Germain prime is 7068555 × 2¹²¹³⁰¹ - 1, discovered by Predrag Minovic in January 2005, using TwinGen and LLR. 2 (two) is a number, numeral, and glyph. ... 3 (three) is a number, numeral, and glyph. ... 5 (five) is a number, numeral, and glyph. ... 11 (eleven) is the natural number following 10 and preceding 12. ... 23 (twenty-three) is the natural number following 22 and preceding 24. ... 29 (twenty-nine) is the natural number following 28 and preceding 30. ... 41 is the natural number following 40 and preceding 42. ... 53 is the natural number following 52 and preceding 54. ... 83 is the natural number following 82 and preceding 84. ... 89 (eighty-nine) is the natural number following 88 and preceding 90. ... 113 is the natural number following 112 and preceding 114. ... 131 is the natural number following 130 and preceding 132. ... 173 is the natural number between 172 and 174. ... 179 is the natural number between 178 and 180. ... 191 is the natural number between 190 and 192. ...

A heuristic estimate for the number of Sophie Germain primes less than n is 2C₂ n / (ln n)² where C₂ is the twin prime constant, approximately 0.660161. For n   =   10⁴, this estimate predicts 156 Sophie Germain primes, which has a 20% error compared to the exact value of 190 above. For n = 10⁷, the estimate predicts 50822, which is still 10% off from the exact value of 56032. Heuristic is the art and science of discovery and invention. ... Look up Number in Wiktionary, the free dictionary A number originally was a count or a measurement. ... The natural logarithm, invented by John Napier, is the logarithm to the base e, where e is equal to 2. ... The twin prime conjecture is a famous problem in number theory that involves prime numbers. ...

A sequence {p, 2p + 1, 2(2p + 1) + 1, ...} of Sophie Germain primes is called a Cunningham chain of the first kind. Every term of such a sequence except the first and last is both a Sophie Germain prime and a safe prime. In mathematics, a Cunningham chain is a certain sequence of prime numbers. ... A safe prime is a prime number of the form 2p + 1, where p is also a prime. ...

It was the eponymous proof in the stage play Proof. An eponym is a person, whether real or fictitious, whose name has (or is thought to have) given rise to the name of a particular place, tribe, discovery, or other item. ... Proof is a play by David Auburn which won the 2001 Pulitzer Prize for Drama and the 2001 Tony Award for Best Play. ...

External references

• The Ten Largest Known Sophie Germain Primes from The Prime Pages
• Sophie-Germain-Primzahl (German Wikipedia)