1989
DOI: 10.1090/s0025-5718-1989-0947470-1
|View full text |Cite
|
Sign up to set email alerts
|

First occurrence prime gaps

Abstract: Abstract.An ongoing search for first occurrence prime gaps continues.An ongoing search for first occurrence prime gaps is being carried out which extends all previous work done on this subject. To date this search has found all such gaps for primes up to 7.263 x 1013. First occurrence prime gaps had previously been known for primes less than 4.444 x 1012 [2]. Several gaps larger than the previously largest gap of 682 (not a first occurrence) found by Weintraub [4] have been found.Computer programs were written… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
2
2

Citation Types

1
18
0

Year Published

1989
1989
2012
2012

Publication Types

Select...
5
3

Relationship

0
8

Authors

Journals

citations
Cited by 24 publications
(19 citation statements)
references
References 5 publications
1
18
0
Order By: Relevance
“…Over 104 blocks of length 8 x 106 each around 5.25 x 1012 (see §4 for a definition), the correlation between maximal values of g(n) and maximal prime gaps in a block was 0.52. The largest value of g(n) that was found, g(n) = 635 for n close to 7r(7.17716 x 1012), is due to the prime gap 674, which is the largest one up to that height ( [3,20]). The second largest value of g(n), g(n) = 589 for n close to 7r(2.61494 x 1012), is due to the prime gap 652, which is also the largest one up to its height.…”
Section: Heuristicsmentioning
confidence: 92%
See 1 more Smart Citation
“…Over 104 blocks of length 8 x 106 each around 5.25 x 1012 (see §4 for a definition), the correlation between maximal values of g(n) and maximal prime gaps in a block was 0.52. The largest value of g(n) that was found, g(n) = 635 for n close to 7r(7.17716 x 1012), is due to the prime gap 674, which is the largest one up to that height ( [3,20]). The second largest value of g(n), g(n) = 589 for n close to 7r(2.61494 x 1012), is due to the prime gap 652, which is also the largest one up to its height.…”
Section: Heuristicsmentioning
confidence: 92%
“…Maximal gaps between consecutive primes around x are thought to be not much larger than (logx)2. (There is a conjecture of Cramer [5] that these gaps are 0((logx)2), and numerical evidence [3,4,20] supports this conjecture as well as a slightly stronger one of Shanks [16]. There are heuristic arguments, based on work of Maier [9], that suggest the true order of magnitude might be slightly larger, but at most by some fractional power of log log x.)…”
Section: Introductionmentioning
confidence: 95%
“…Over 104 blocks of length 8 x 106 each around 5.25 x 1012 (see §4 for a definition), the correlation between maximal values of g(n) and maximal prime gaps in a block was 0.52. The largest value of g(n) that was found, g(n) = 635 for n close to 7r(7.17716 x 1012), is due to the prime gap 674, which is the largest one up to that height ( [3,20]). The second largest value of g(n), g(n) = 589 for n close to 7r(2.61494 x 1012), is due to the prime gap 652, which is also the largest one up to its height.…”
Section: Heuristicsmentioning
confidence: 98%
“…Maximal gaps between consecutive primes around x are thought to be not much larger than (logx)2. (There is a conjecture of Cramer [5] that these gaps are 0((logx)2), and numerical evidence [3,4,20] supports this conjecture as well as a slightly stronger one of Shanks [16]. There are heuristic arguments, based on work of Maier [9], that suggest the true order of magnitude might be slightly larger, but at most by some fractional power of log log x.)…”
Section: Introductionmentioning
confidence: 97%
“…What then is the largest x so that all primes up to x have ever been formed and studied in a computer memory? Young and Potier [10] have computed all primes up to 7.2635 x 10 13 and studied the gaps between consecutive primes. Their record-making calculations are still continuing now.…”
mentioning
confidence: 99%