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A050249 Weakly prime numbers (changing any one decimal digit always produces a composite number). 15
294001, 505447, 584141, 604171, 971767, 1062599, 1282529, 1524181, 2017963, 2474431, 2690201, 3085553, 3326489, 4393139, 5152507, 5564453, 5575259, 6173731, 6191371, 6236179, 6463267, 6712591, 7204777, 7469789, 7469797 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Tao proved that this sequence is infinite. - T. D. Noe, Mar 01 2011

For the following values 5, 6, 7, 8, 9, 10 of k, the number of terms < 10^k in this sequence is 0, 5, 35, 334, 3167, 32323. - Jean-Marc Rebert, Nov 10 2015

LINKS

Klaus Brockhaus and Jean-Marc Rebert, Table of n, a(n) for n = 1..3167 (first 1317 terms from Klaus Brockhaus)

Jackson Hopper, Paul Pollack, Digitally delicate primes, arXiv:1510.03401 [math.NT], 2015.

Terence Tao, A remark on primality testing and decimal expansions, Journal of the Australian Mathematical Society 91:3 (2011), pp. 405-413.

Eric Weisstein's World of Mathematics, Weakly Prime

MATHEMATICA

fQ[n_] := Block[{d = IntegerDigits@ n, t = {}}, Do[AppendTo[t, FromDigits@ ReplacePart[d, i -> #] & /@ DeleteCases[Range[0, 9], x_ /; x == d[[i]]]], {i, Length@ d}]; ! AnyTrue[Flatten@ t, PrimeQ]] ; Select[Prime@ Range[10^5], fQ] (* Michael De Vlieger, Nov 10 2015, Version 10 *)

PROG

(MAGMA) IsA118118:=function(n); D:=Intseq(n); return forall{ <k, j>: k in [1..#D], j in [0..9] | j eq D[k] or not IsPrime(Seqint(S)) where S:=Insert(D, k, k, [j]) }; end function; [ p: p in PrimesUpTo(8000000) | IsA118118(p) ]; // Klaus Brockhaus, Feb 28 2011

(PARI) isokp(n) = {v = digits(n); for (k=1, #v, w = v; for (j=0, 9, if (j != v[k], w[k] = j; ntest = subst(Pol(w), x, 10); if (isprime(ntest), return(0)); ); ); ); return (1); }

lista(nn) = {forprime(p=2, nn, if (isokp(p), print1(p, ", ")); ); } \\ Michel Marcus, Dec 15 2015

CROSSREFS

Cf. A118118, A158124 (weakly primes), A158125 (weakly primes)

Cf. A137985 (analogous base 2 sequence), A186995 (weak primes in base n).

Sequence in context: A255754 A254843 A158124 * A224973 A182206 A178997

Adjacent sequences:  A050246 A050247 A050248 * A050250 A050251 A050252

KEYWORD

nonn,base

AUTHOR

Eric W. Weisstein

EXTENSIONS

Edited by Charles R Greathouse IV, Aug 02 2010

STATUS

approved

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Last modified February 9 12:54 EST 2016. Contains 268123 sequences.