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Search: id:A111943
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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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+0
3
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| 13, 23, 113, 1327, 31397, 370261, 2010733, 20831323, 25056082087, 2614941710599, 19581334192423, 218209405436543, 1693182318746371
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Primes less than 23 are anomalous and are excluded.
The sequence ends with Bertil Nyman's 1999 discovery.
Shanks conjecture is that the ratio will never reach 1.
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REFERENCES
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R. K. Guy, Unsolved Problems in Theory of Numbers, Springer-Verlag, Third Edition, 2004, A8.
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LINKS
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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
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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
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Cf. A111870.
Cf. A166363.
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KEYWORD
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nonn,hard,new
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AUTHOR
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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
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Corrected and edited (p_n could be misinterpreted as the n_th prime) by Daniel Forgues (squid(AT)zensearch.com), Nov 20 2009
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