Revision History for A158594
(Underlined text is an addition;
strikethrough text is a deletion.)
Showing entries 1-10
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#19 by Peter Luschny at Mon Jul 29 11:57:37 EDT 2019
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#18 by Joerg Arndt at Mon Jul 29 10:00:01 EDT 2019
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#17 by Jon E. Schoenfield at Sun Jul 28 21:30:09 EDT 2019
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#16 by Jon E. Schoenfield at Sun Jul 28 21:29:59 EDT 2019
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| COMMENTS
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4) Sequence is part of A068674 a(n) n=1,...,30: 14 first 14 primes: 7, 11, 17, 31, 37, 73, 271, 331, 359, 373, 673, 733, 2297, 3461.
5) Note the "world record" 2297: smallest prime which yields five other primes 32297,, 23297,, 22397,, 22937,, 22973.
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| CROSSREFS
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Cf. A068674, Numbers which yieldsyield primes when a 3 is prefixed or appended.
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| STATUS
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approved
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#15 by Michel Marcus at Sat Feb 02 03:18:53 EST 2019
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#14 by Joerg Arndt at Sat Feb 02 02:34:44 EST 2019
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#13 by Jinyuan Wang at Sat Feb 02 00:21:50 EST 2019
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#12 by Jinyuan Wang at Sat Feb 02 00:21:46 EST 2019
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| LINKS
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Jinyuan Wang, <a href="/A158594/b158594.txt">Table of n, a(n) for n = 1..500</a>
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| PROG
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(PARI) isok(n)={i=#digits(n); m=1; k=0; while(k<i+1&&m==1, r=n\10^k; s=n-r*10^k; t=r*10^(k+1)+s+3*10^k; if(isprime(t)==0, m=0); k++); m; } \\ Jinyuan Wang, Feb 02 2019
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| STATUS
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proposed
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#11 by Jon E. Schoenfield at Fri Feb 01 22:27:56 EST 2019
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#10 by Jon E. Schoenfield at Fri Feb 01 20:46:37 EST 2019
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| EXAMPLE
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1) 109 is not noa memberterm: 3109,, 1039,, 1093 are primes, but 1309 = 7 x * 11 x * 17.
2) 121 is a term: 3121 (3 prefixed), 1213 (3 appended), 1321 and 1231 (3 inserted) are primes.
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| MAPLE
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Lton := proc(L) local i ; add(op(i, L)*10^(i-1), i=1..nops(L) ) ; end: isA158594 := proc(n) local dgs, i, p; dgs := convert(n, base, 10) ; p := [3, op(dgs)] ; if not isprime(Lton(p)) then RETURN(false) ; fi; p := [op(dgs), 3] ; if not isprime(Lton(p)) then RETURN(false) ; fi; for i from 1 to nops(dgs)-1 do p := [op(1..i, dgs), 3, op(i+1..nops(dgs), dgs)] ; if not isprime(Lton(p)) then RETURN(false) ; fi; od: RETURN(true) ; end: for n from 1 to 25000 do if isA158594(n) then printf("%d, ", n) ; fi; od: [From _: # _R. J. Mathar_, Mar 26 2009]
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| CROSSREFS
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Cf. A068674 , Numbers which yields primes when a 3 is prefixed or appended.
Cf. A068679 , Numbers which yield a prime whenever a 1 is inserted anywhere in them (including at the beginning or end).
Cf. A158232 , Numbers which yield primes when "13" is prefixed or appended.
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| STATUS
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approved
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