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1. en.wikipedia.org › wiki › Safe_and_Sophie_Germain_primesSafe and Sophie Germain primes - Wikipedia

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   The number 2p + 1 associated with a Sophie Germain prime is called a safe prime. For example, 11 is a Sophie Germain prime and 2 × 11 + 1 = 23 is its associated safe prime. Sophie Germain primes and safe primes have applications in public key cryptography and primality testing.

2. artofproblemsolving.com › Sophie_Germain_IdentitySophie Germain Identity - Art of Problem Solving

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   Find the largest prime factor of , given that it is the product of three distinct primes. (ARML 2016 Individual #10) Prove that there exist infinite natural numbers fulfilling the following property: For all natural numbers , is not a prime number. (IMO 1969 #1) See Also. MacTutor biography of Sophie Germain

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4. mathworld.wolfram.com › SophieGermainPrimeSophie Germain Prime -- from Wolfram MathWorld

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   A prime is said to be a Sophie Germain prime if both and are prime. The first few Sophie Germain primes are 2, 3, 5, 11, 23, 29, 41, 53, 83, 89, 113, 131, ... (OEIS A005384 ). It is not known if there are an infinite number of Sophie Germain primes (Hoffman 1998, p. 190).

5. sitn.hms.harvard.edu › flash › 2017(2 x prime) + 1 = ? :The 200-year-old story of Sophie Germain ...

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   Jun 14, 2017 · The original primes that yielded new primes in this fashion are called “Sophie Germain Primes” (e.g. 2, 3, 5, 11), a set of numbers whose discovery is credited to Sophie. In general, a Sophie Germain Prime is defined as a prime “s” such that (2 × s) + 1 is also a prime. Figure 1: Summary of the different categories of integer numbers ...

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7. www.math.uci.edu › ~ndonalds › math180b6 Sophie Germain and Fermat’s Last Theorem

   www.math.uci.edu › ~ndonalds › math180b

   Germain considered primes related to p, so-called auxiliary primes. The existence of such can be used to show that solutions to xp + yp = zp must have certain properties. Definition 6.1. Let p be an odd prime. An auxiliary prime to p is any prime of the form q = 2kp + 1 where k 2 N.

8. mathshistory.st-andrews.ac.uk › Biographies › GermainSophie Germain (1776 - 1831) - Biography - MacTutor History ...

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   Apr 1, 2012 · Quick Info. Born. 1 April 1776. Paris, France. Died. 27 June 1831. Paris, France. Summary. Sophie Germain made a major contributions to number theory (in particular, the theory of primes), acoustics and elasticity. View ten larger pictures. Biography.

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   What are Sophie Germain primes?

   • The original primes that yielded new primes in this fashion are called “Sophie Germain Primes” (e.g. 2, 3, 5, 11 ), a set of numbers whose discovery is credited to Sophie. In general, a Sophie Germain Prime is defined as a prime “ s ” such that (2 × s) + 1 is also a prime. Figure 1: Summary of the different categories of integer numbers.

   (2 x prime) + 1 = ? :The 200-year-old story of Sophie Germain and its

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   Are Sophie Germain primes safe?

   • Safe primes are fundamental in the field of cryptography, which means that the Sophie Germain Primes form the foundation that underlies today’s security systems. It would be fun to imagine what Sophie would feel, if she were alive to know that her enthusiasm toward math has become a central pillar supporting 21st century technology.

   (2 x prime) + 1 = ? :The 200-year-old story of Sophie Germain and its

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   How did Sophie Germain prove Fermat's Last Theorem?

   • Around 1825, Sophie Germain proved that the first case of Fermat's last theorem is true for such primes, i.e., if is a Sophie Germain prime, then there do not exist integers , , and different from 0 and none a multiple of such that Caldwell, C. K. "Prime Pages.

   Sophie Germain Prime -- from Wolfram MathWorld

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   What if p is a Germain prime?

   • Definition 6.1. Let p be an odd prime. An auxiliary prime to p is any prime of the formq= 2kp +1 where k 2N. A prime p such that 2p +1 is prime is called a Germain prime. It is unknown if there are infinitely many of these. We give Germain’s proof of case 1 of Fermat’s Last Theorem whenever p is a Germain prime.

   6 Sophie Germain and Fermat’s Last Theorem - University of California

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10. en.wikipedia.org › wiki › Sophie_GermainSophie Germain - Wikipedia

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    A Sophie Germain prime is a prime p such that 2p + 1 is also prime. The Germain curvature (also called mean curvature) is (+) /, where k 1 and k 2 are the maximum and minimum values of the normal curvature. Sophie Germain's identity states that for any {x, y},