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A111943
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Prime p with prime gap q-p of n-th record Cramer-Shanks-Granville ratio, where q is smallest prime larger than p and C-S-G ratio is (q-p)/(log(p))^2.
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3
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13, 23, 113, 1327, 31397, 370261, 2010733, 20831323, 25056082087, 2614941710599, 19581334192423, 218209405436543, 1693182318746371
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The sequence ends with Bertil Nyman's 1999 discovery.
Shanks conjecture is that the ratio will never reach 1.
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REFERENCES
| R. K. Guy, Unsolved Problems in Theory of Numbers, Springer-Verlag, Third Edition, 2004, A8.
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LINKS
| Eric Weisstein's World of Mathematics, Prime Gaps.
Eric Weisstein's World of Mathematics, Cramer-Granville Conjecture.
Eric Weisstein's World of Mathematics, Shanks Conjecture (and Wolf Conjecture.)
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EXAMPLE
| n Ratio prime:
2 0.6103 23
3 0.6264 113
4 0.6575 1327
5 0.6715 31397
6 0.6812 370261
7 0.7025 2010733
8 0.7394 20831323
9 0.7953 25056082087
10 0.7975 2614941710599
11 0.8177 19581334192423
12 0.8311 218209405436543
13 0.9206 1693182318746371
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CROSSREFS
| Cf. A111870, A166363, A002386.
Sequence in context: A147443 A131447 A110196 * A039448 A089768 A185684
Adjacent sequences: A111940 A111941 A111942 * A111944 A111945 A111946
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KEYWORD
| nonn,hard
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), following emails from R. K. Guy and Ed Pegg, Jr., Nov 27 2005
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EXTENSIONS
| Corrected and edited (p_n could be misinterpreted as the n-th prime) by Daniel Forgues (squid(AT)zensearch.com), Nov 20 2009
Edited by Charles R Greathouse IV (charles.greathouse(AT)case.edu), May 14 2010
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