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Prime Numbers and Goldbach Conjecture


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1 Department of Mathematics, Govt. College Bilaspur (H.P.)-174001, India
     

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In this paper, two laws relating to prime numbers have been given. An attempt has been made to prove the Goldbach’s conjecture that every even natural number greater than or equal to 4 can be expressed as a sum of two prime numbers. A result relating to counting of prime and composite numbers within the range from 1 to n has also been presented here.
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  • Goldbach, C. (1742) Letter to Euler, 7 June.

  • Renyi, A. (1962). On the representation of an even number as the sum of a single prime and a single almost-prime number. Amer. Math. Soc. Transl. 19(2): 299-321.

  • Schnirelmann, L. (1930) On additive properties of numbers. Izv. Donskowo Politechn. Inst. (Nowotscherkask), 14(2-3):3-28.

  • Shen, Mok-Kong (1964) On checking the Goldbach conjecture. Nordisk Tidskr. Informations –Behandling, 4: 243-245; MR 30, #3051.

  • Vinogradov, I. M. (1937) The representation of an odd number as the sum of three primes. Dokl. Akad. Nauk SSSR, 16: 139-142.

  • Yin, Wen-lin (1956) Note on the representation of large integers as sums of primes. Bull. Acad. Polon. Sci. CI. III, 4: 793-795; MR 19, 16.


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  • Prime Numbers and Goldbach Conjecture

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Authors

Jagjit Singh
Department of Mathematics, Govt. College Bilaspur (H.P.)-174001, India

Abstract


In this paper, two laws relating to prime numbers have been given. An attempt has been made to prove the Goldbach’s conjecture that every even natural number greater than or equal to 4 can be expressed as a sum of two prime numbers. A result relating to counting of prime and composite numbers within the range from 1 to n has also been presented here.

References