On Problems Related to Primes: Some Ideas

Details On Problems Related to Primes: Some Ideas On Problems Related to Primes: Some Ideas

2005-10-13

arxiv.org/abs/math/0510277v1

Mathematics

General Mathematics

41 pages

Scientific paper

We present some new ideas on important problems related to primes. The topics of our discussion are: simple formulae for primes, twin primes, Sophie Germain primes, prime tuples less than or equal to a predefined number, and their infinitude; establishment of a kind of similarity between natural numbers and numbers that appear in an arithmetic progression, similar formulae for primes and the so called generalized twin primes in an arithmetic progression and their infinitude; generalization of Bertrand postulate and a Bertrand like postulate for twin primes; some elementary implications of a simple primality test, the use of Chinese remainder theorem in a possible proof of the Goldbach conjecture; Schinzel Sierpinski conjecture; and lastly the Mersenne primes and composites, Fermat primes, and their infinitude.

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