LOGICVILLE

Mathematical Puzzles

Dual Cryptograms

Cryptarithms
Anagrams Cryptograms Doublets
Logic Puzzles Magic Word Squares Sudoku
Chess Fractal Puzzles Tangrams

 

 

 

Intellectual Puzzles
Bookstore
List of Puzzles
Analytical Puzzles
Christmas Puzzles
New Year's Puzzles
Fractal Puzzles
Easter Puzzles
Nature Fractals
Encrypted Quotations
Fractal Images
Baseball Puzzles
Daily Fractal Puzzle
Math Recreations
Algebra Placement
Cryptogram Challenge
Sudoku
Tangrams
Tangram Stories
Puzzle Categories
Thanksgiving Quotes
Christmas Quotes
Christmas Logic
New Year Resolutions
Solutions
Advertise With Us

 

 

Previous Topic

Next Topic

SOPHIE GERMAIN PRIMES

A Sophie Germain Prime is a prime number P for which 2P+1 is also a prime.  These prime numbers include:

     2, 3, 5, 11, 23, 29, 41, 53, 89, 113, 131...

It can be noted that a Sophie Germain prime p > 3 is of the form 6k−1, since adding one to them make them a multiple of six.

These primes were named after the French mathematician Marie-Sophie Germain when she (around 1825) proved that Fermat's Last Theorem holds true for these primes.  That is, if n is a Sophie Germain prime greater than 2, then there are no whole numbers a, b, c such that

an + bn = cn.

It has been conjectured that there are infinitely many Sophie Germain primes, however, this conjecture has not yet been proven.

The corresponding prime numbers of the form 2P+1, where P is a Sophie Germain prime are called safe primes.

 

 

More Mathematical Recreations

Enjoy these other topics in mathematics:

MARSENNE'S PRIME

PERFECT NUMBERS

PLATONIC SOLIDS 

MOBIUS STRIP 

PRIME NUMBERS

GOLDEN RATIO

PI

FERMAT'S LAST THEOREM

SPIRALS

PYTHAGOREAN TRIPLETS

EULER'S CONSTANT

FIBONACCI SERIES

EQUIANGULAR SPIRAL

GREGORIAN CALENDAR

SUDOKU

HARMONIC TRIANGLE

SUM OF SQUARES

SAFE PRIMES

FRACTALS

MANDELBROT SET

CHINESE NEW YEAR

EULER PATH

GOLDEN TRIANGLE

HAMILTONIAN CYCLE

FOUR COLOR THEOREM

CHINESE POSTMAN PROBLEM

CANTOR SET

AN UNPREDICTABLE EVENT

MAGIC SQUARES

PASCAL TRIANGLE

GOLDEN RECTANGLE

GOLDEN TRIANGLE

HYPERBOLA

FOUR SQUARE THEOREM

 

 

Previous Topic

Next Topic

 

Custom Search

MX iTunes, App Store, iBookstore, and Mac App Store

 

Hosted By Web Hosting by PowWeb

2000-2013 Logicville