Analysis of Successive Occurrence of Digit 1
in Prime Numbers till 1 Trillion

Neeraj Anant Pande

doi:https://doi.org/10.14445/22315373/IJMTT-V38P522

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 38 | Number 3 | Year 2016 | Article Id. IJMTT-V38P522 | DOI : https://doi.org/10.14445/22315373/IJMTT-V38P522

Analysis of Successive Occurrence of Digit 1 in Prime Numbers till 1 Trillion

Neeraj Anant Pande

Citation :

Neeraj Anant Pande, "Analysis of Successive Occurrence of Digit 1 in Prime Numbers till 1 Trillion," International Journal of Mathematics Trends and Technology (IJMTT), vol. 38, no. 3, pp. 125-129, 2016. Crossref, https://doi.org/10.14445/22315373/IJMTT-V38P522

Abstract

Primes less than 1 trillion are probed for successive occurrence of digit 1 in them. Multiple successive occurrences of 1’s are analyzed. The first and last prime numbers containing successive repetitions of various number of 1’s are determined within initial 12 ranges of increasing powers of 10.

Keywords

Prime numbers, digit 1, successive occurrences.

References

[1] Benjamin Fine, Gerhard Rosenberger, ―Number Theory: An Introduction via the Distribution of Primes, Birkhauser, 2007.
[2] Neeraj Anant Pande, ―Numeral Systems of Great Ancient Human Civilizations, Journal of Science and Arts, Year 10, No. 2 (13), (2010), pp. 209-222.
[3] Neeraj Anant Pande, ―Improved Prime Generating Algorithms by Skipping Composite Divisors and Even Numbers (Other Than 2), Journal of Science and Arts, Year 15, No.2(31), (2015), 135-142.
[4] Neeraj Anant Pande, ―Analysis of Primes Less Than a Trillion, International Journal of Computer Science and Engineering Technology, Vol. 6, No 6, (2015), pp. 332-341.
[5] Neeraj Anant Pande, ―Analysis of Occurrence of Digit 0 in Natural Numbers Less Than 10n, American International Journal of Research in Formal, Applied and Natural Sciences, Communicated, 2016.
[6] Neeraj Anant Pande, ―Analysis of Successive Occurrence of Digit 0 in Natural Numbers Less Than 10 n, IOSR-Journal of Mathematics, Accepted, 2016.
[7] Neeraj Anant Pande, ―Analysis of Non-successive Occurrence of Digit 0 in Natural Numbers Less Than 10n, International Journal of Emerging Technologies in Computational and Applied Sciences, Communicated, 2016.
[8] Neeraj Anant Pande, ―Analysis of Occurrence of Digit 0 in Prime Numbers till 1 Trillion, Journal of Research in Applied Mathematics, Accepted, 2016.
[9] Neeraj Anant Pande, ―Analysis of Successive Occurrence of Digit 0 in Prime Numbers till 1 Trillion, International Journal of Mathematics And its Applications, Communicated, 2016.
[10] Neeraj Anant Pande, ―Analysis of Non-successive Occurrence of Digit 0 in Prime Numbers till 1 Trillion, International Journal of Computational and Applied Mathematics, Communicated, 2016.
[11] Neeraj Anant Pande, ―Analysis of Occurrence of Digit 1 in Natural Numbers Less Than 10 n, Advances in Theoretical and Applied Mathematics, 11(2) (2016), 99-104.
[12] Neeraj Anant Pande, ―Analysis of Successive Occurrence of Digit 1 in Natural Numbers Less Than 10 n, American International Journal of Research in Science, Technology, Engineering and Mathematics, 16(1), (2016), 37-41.
[13] Neeraj Anant Pande, ―Analysis of Non-successive Occurrence of Digit 1 in Natural Numbers Less Than 10n, International Journal of Advances in Mathematics and Statistics, Communicated, 2016.
[14] Neeraj Anant Pande, ―Analysis of Occurrence of Digit 1 in Prime Numbers till 1 Trillion, International Research Journal of Mathematics, Engineering and IT, Communicated, 2016.