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Search: id:A140515
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| A140515 |
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Rounding up or rounding down decimal expansions of n+1 digits of Pi give provable prime numbers for these values of n. |
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+0
1
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OFFSET
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0,3
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COMMENT
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Proofs of the primality of decimal expansions ending at n= 601, 1901 and 2394 are given at marvinrayburns.com.
The next candidates are 3970,5826 and 16207 but, as far as I know, their primality has not been proved.
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LINKS
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Carlos B. Rivera F. Approximation to pi with primes.
Weisstein, Eric W., Pi Digits
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EXAMPLE
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10^0*Pi=3.1... =p0. Floor(p0)=3. 3 and is prime, so the first element in the sequence is 0.
10^1*Pi=31.4...=p1. Floor(p1)=31. 31 is prime, so the second element in the sequence is 1.
10^5*Pi=314159.2...=p1. Floor(p1)=314159. 314159 is prime, so the third element in the sequence is 5.
10^11*Pi=314159265358.9...=p2. Ceiling(p2)=314159265359. 314159265359 is prime, so the fourth element in the sequence is 11.
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CROSSREFS
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Sequence in context: A140697 A048253 A102174 this_sequence A056996 A102184 A084720
Adjacent sequences: A140512 A140513 A140514 this_sequence A140516 A140517 A140518
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KEYWORD
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nonn,uned
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AUTHOR
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Marvin Ray Burns (bmmmburns(AT)sbcglobal.net), Jul 01 2008, Jul 02 2008
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