A089395 Prime productive numbers m: Let the digits of m be abcd. Then the numbers bcd*a+1, cd*ab+1, d*abc+1, abcd+1 etc. are all primes. If m is a k-digit number it produces k such primes.
1, 2, 4, 6, 12, 16, 22, 28, 36, 52, 58, 66, 82, 106, 112, 136, 166, 178, 256, 306, 336, 352, 448, 502, 508, 556, 562, 586, 616, 652, 658, 718, 982, 1018, 1108, 1162, 1192, 1228, 1498, 1708, 2002, 2026, 2086, 2686, 2776, 2998, 3136, 3412, 3526, 3592, 4078, 4918
Offset: 0
Examples
256 is a term as 2*56 + 1 = 113, 25*6 + 1 = 151 and 256 + 1 = 257 are all primes.
Links
- Harvey P. Dale, Table of n, a(n) for n = 0..139 (all terms up to 1 million)
Programs
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Maple
with(combinat): ds:=proc(s) local j: RETURN(add(s[j]*10^(j-1),j=1..nops(s))):end: for d from 1 to 6 do sch:=[seq([1,op(i),d+1],i=[[],seq([j],j=2..d)])]: for n from 10^(d-1) to 10^d-1 do sn:=convert(n,base,10): fl:=0: for s in sch do m:=mul(j,j=[seq(ds(sn[s[i]..s[i+1]-1]),i=1..nops(s)-1)])+1: if not isprime(m) then fl:=1: break fi od: if fl=0 then printf("%d, ",n) fi od od: # C. Ronaldo -
Mathematica
ppnQ[n_]:=Mod[n,10]!=0&&AllTrue[Times@@@Table[FromDigits/@TakeDrop[ IntegerDigits[ n],k]/.(0->1),{k,IntegerLength[n]}]+1,PrimeQ]; Select[Range[5000], ppnQ] (* The program uses the AllTrue and TakeDrop functions from Mathematica version 10 *) (* Harvey P. Dale, Mar 23 2019 *)
Extensions
Corrected and extended by C. Ronaldo (aga_new_ac(AT)hotmail.com), Dec 25 2004
Comments