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A217045
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Primes that remain prime when a single "4" digit is inserted between any two adjacent decimal digits.
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4
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19, 37, 43, 61, 67, 73, 97, 109, 199, 211, 223, 241, 349, 409, 421, 457, 463, 541, 571, 751, 757, 823, 991, 1033, 1087, 1321, 1423, 1447, 1543, 2749, 3361, 3469, 3499, 3847, 4111, 4273, 4483, 5059, 5437, 5443, 5449, 6373, 6709, 6793, 7687, 8089, 8221, 8443
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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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87697 is prime and also 876947, 876497, 874697 and 847697.
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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, 1500]], AllTrue[Table[FromDigits[Insert[ IntegerDigits[ #], 4, n]], {n, 2, IntegerLength[#]}], PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Dec 04 2017 *)
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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]=4; 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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