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A217065
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Primes that remain prime when a single "7" digit is inserted between any two adjacent digits.
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9
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13, 19, 67, 73, 97, 277, 367, 379, 421, 433, 487, 541, 691, 757, 853, 967, 1117, 1471, 1747, 2017, 2617, 2749, 2851, 2953, 3463, 3529, 3571, 4507, 5077, 5923, 6073, 6079, 6343, 6481, 6577, 6709, 6829, 6967, 7351, 7417, 7573, 7681, 8317, 8719, 9157, 9649, 13177
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OFFSET
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1,1
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LINKS
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EXAMPLE
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311683 is prime and also 3116873, 3116783, 3117683, 3171683 and 3711683.
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MAPLE
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with(numtheory);
local a, b, c, i, n, ok;
for n from 5 to q do
a:=ithprime(n); b:=0; while a>0 do b:=b+1; a:=trunc(a/10); od; a:=ithprime(n); ok:=1;
for i from 1 to b-1 do
c:=a+9*10^i*trunc(a/10^i)+10^i*x; if not isprime(c) then ok:=0; break; fi; od;
if ok=1 then print(ithprime(n)); fi; od; end:
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MATHEMATICA
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Select[Prime[Range[5, 1600]], AllTrue[FromDigits/@Table[Insert[ IntegerDigits[ #], 7, i], {i, 2, IntegerLength[#]}], PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Oct 12 2016 *)
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PROG
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(PARI) is(n)=my(v=concat([""], digits(n))); for(i=2, #v-1, v[1]=Str(v[1], v[i]); v[i]=7; if(i>2, v[i-1]=""); if(!isprime(eval(concat(v))), return(0))); isprime(n) \\ Charles R Greathouse IV, Sep 26 2012
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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