publication . Preprint . 2016

On the last digits of consecutive primes

Holt, Fred B.;
Open Access English
  • Published: 08 Apr 2016
Recently Oliver and Soundararajan made conjectures based on computational enumerations about the frequency of occurrence of pairs of last digits for consecutive primes. By studying Eratosthenes sieve, we have identified discrete dynamic systems that exactly model the populations of gaps across stages of Eratosthenes sieve. Our models provide some insight into the observed biases in the occurrences of last digits in consecutive primes, and the models suggest that the biases will ultimately be reversed for large enough primes. The exact model for populations of gaps across stages of Eratosthenes sieve provides a constructive complement to the probabilistic models ...
arXiv: Mathematics::Number TheoryMathematics::General Mathematics
free text keywords: Mathematics - Number Theory, 11N05, 11A41, 11B75, 11A07
Download from

1. R. Brent, The distribution of small gaps between successive prime numbers, Math. Comp. 28 (1974), 315{324. [OpenAIRE]

2. G.H. Hardy and J.E. Littlewood, Some problems in 'partitio numerorum' iii: On the expression of a number as a sum of primes, G.H. Hardy Collected Papers, vol. 1, Clarendon Press, 1966, pp. 561{630.

3. F.B. Holt and H. Rudd, On Polignac's conjecture, arXiv:1402.1970v2, 15 Feb 2014.

4. F.B. Holt with H. Rudd, Combinatorics of the gaps between primes, arXiv:1510.00743v2, 8 Oct 2015.

5. Mathematicians discover prime conspiracy, Quanta Magazine, 13 March 2016.

6. R.J.L. Oliver and K. Soundararajan, Unexpected biases in the distribution of consecutive primes, arXiv:1603.30720, version 2, 15 March 2016.

Models for g=30 Models for g=420 0.04 0.08

Powered by OpenAIRE Research Graph
Any information missing or wrong?Report an Issue