A186694 Numbers ending in 1, 3, 7 or 9 such that changing any one decimal digit produces a composite number.

212159, 294001, 505447, 584141, 595631, 604171, 872897, 971767, 1062599, 1203623, 1282529, 1293671, 1524181, 1566691, 1702357, 1830661, 2017963, 2474431, 2690201, 3085553, 3326489, 3716213, 3964169, 4103917, 4134953, 4173921, 4310617, 4376703

Offset: 1

Author

Arkadiusz Wesolowski, Feb 25 2011

Keywords

• base
• nonn

Comments

Union of A050249 and A143641.

This sequence is infinite because Terence Tao proved that sequence A050249 is infinite.

Links

• Arkadiusz Wesolowski, Table of n, a(n) for n = 1..1500
• Chris Caldwell, The Prime Glossary, Weakly prime
• G. L. Honaker, Jr. and Chris Caldwell, Prime Curios! 212159
• G. L. Honaker, Jr. and Chris Caldwell, Prime Curios! 17171...58369 (1000-digits)
• Terence Tao, A remark on primality testing and decimal expansions, Journal of the Australian Mathematical Society 91:3 (2011), pp. 405-413.

Crossrefs

Cf. A050249, A045572, A143641.

Programs

Mathematica

primeProof[n_] := Module[{d, e, isPP, num}, d=IntegerDigits[n]; isPP=True; Do[e=d; e[[i]]=j; num=FromDigits[e]; If[num != n && PrimeQ[num], isPP=False; Break[]], {i, Length[d]}, {j, 0, 9}]; isPP]; Select[Range[1, 1000000, 2], Mod[#, 5] > 0 && primeProof[#] &] (* T. D. Noe, Feb 26 2011 *)