A164328
a(n) is the smallest n-digit prime term of A158594 and zero if there is no such number.
Original entry on oeis.org
7, 11, 271, 1033, 18289, 133733, 1045493, 11939237, 103333333, 1342313221, 10300335833, 145933933339, 1332523411733, 11653733331833
Offset: 1
a(5)=18289 so all the seven numbers 18289, 318289, 138289, 183289, 182389,
182839 & 182893 are primes.
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pp[n_, k_] := Catch[Block[{d = IntegerDigits@n}, Do[If[! PrimeQ[ FromDigits[ Insert[d, k, i]]], Throw[False]], {i, 1+Length@d}]; True]]; a[n_] := Catch[ Block[{p = NextPrime[10^(n-1)]}, While[p < 10^n, If[pp[p, 3], Throw@p, p = NextPrime@p]]; 0]]; a /@ Range[8] (* Giovanni Resta, Aug 13 2013 *)
A228148
a(n) is the smallest n-digit prime which remains prime whenever a 1 is inserted, appended or prepended, or 0 if no such prime exists.
Original entry on oeis.org
3, 13, 103, 1117, 11119, 114031, 1114693, 11213611, 101116111, 1013251111, 10116171733, 101346411811, 1011670114111, 11111117116117
Offset: 1
a(3) = 103 is the smallest 3-digit prime which yields 4 primes by inserting a 1 in every possible position: 1103, 1103, 1013, 1031.
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pp[n_, k_] := Catch[Block[{d = IntegerDigits@n}, Do[If[! PrimeQ[ FromDigits[ Insert[d, k, i]]], Throw[False]], {i, 1+Length@d}]; True]]; a[n_] := Catch[ Block[{p = NextPrime[10^(n-1)]}, While[p < 10^n, If[pp[p, 1], Throw@p, p = NextPrime@p]]; 0]]; a /@ Range[7]
A228149
a(n) is the smallest n-digit prime which remains prime whenever a 7 is inserted, appended or prepended, or 0 if no such prime exists.
Original entry on oeis.org
3, 19, 433, 1471, 13177, 175687, 1740787, 10871017, 137725897, 1670181787, 12845952529, 117777772309, 1008078796477, 11777787780727
Offset: 1
a(3) = 433 is the smallest 3-digit prime which yields 4 primes by inserting a 7 in every possible position: 7433, 4733, 4373, 4337.
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pp[n_, k_] := Catch[Block[{d = IntegerDigits@n}, Do[If[! PrimeQ[ FromDigits[ Insert[d, k, i]]], Throw[False]], {i, 1+Length@d}]; True]]; a[n_] := Catch[ Block[{p = NextPrime[10^(n-1)]}, While[p < 10^n, If[pp[p, 7], Throw@p, p = NextPrime@p]]; 0]]; a /@ Range[8]
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