Why Did Sophie Germain Discover Germain Primes?

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SUMMARY

Sophie Germain discovered Germain primes as part of her work on Fermat's Last Theorem, specifically proving the first case where the exponent divides one of the bases. Her findings confirmed the theorem's validity for every Sophie Germain prime and extended similar proofs to all primes up to 100. For comprehensive insights, refer to Harold M. Edwards' 2000 publication, "Fermat's Last Theorem: A Genetic Introduction to Algebraic Number Theory."

PREREQUISITES
  • Understanding of Fermat's Last Theorem
  • Familiarity with prime numbers and their classifications
  • Basic knowledge of algebraic number theory
  • Awareness of mathematical proofs and their methodologies
NEXT STEPS
  • Explore the implications of Sophie Germain primes in modern number theory
  • Study the complete proof of Fermat's Last Theorem by Andrew Wiles
  • Investigate applications of Germain primes in cryptography
  • Learn about the history and contributions of Sophie Germain to mathematics
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Mathematicians, number theorists, educators, and students interested in the historical context and applications of prime numbers and Fermat's Last Theorem.

matqkks
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Why did Germain come up with her Germain primes? I am intrigued to know why Sophie came across these primes. Do they have any applications?
 
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According to wikipedia:

Germain proved that the first case of Fermat's Last Theorem, in which the exponent divides one of the bases, is true for every Sophie Germain prime, and she used similar arguments to prove the same for all other primes up to 100. For details see Edwards, Harold M. (2000), Fermat's Last Theorem: A Genetic Introduction to Algebraic Number Theory

http://en.wikipedia.org/wiki/Sophie_Germain_prime
 

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