A243411 Least prime p such that p*10^n-1, p*10^n-3, p*10^n-7 and p*10^n-9 are all prime.
2, 2, 10193, 24851, 20549, 719, 22133, 230471, 46679, 432449, 114689, 227603, 305297, 61463, 1866467, 866309, 1189403, 362081, 2615783, 493433, 966353, 4154363, 6562931, 9096203, 3701627, 3128813, 20983727, 303593, 24437537, 1068491
Offset: 1
Keywords
Programs
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Mathematica
lpp[n_]:=Module[{p=2,c=10^n},While[!AllTrue[p*c-{1,3,7,9}, PrimeQ], p= NextPrime[ p]];p]; Array[lpp,30] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jun 12 2016 *) -
PARI
a(n)=for(k=1,10^8,if(ispseudoprime(prime(k)*10^n-1) && ispseudoprime(prime(k)*10^n-3) && ispseudoprime(prime(k)*10^n-7) && ispseudoprime(prime(k)*10^n-9), return(prime(k)))) n=1;while(n<100,print1(a(n),", ");n++)
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Python
import sympy from sympy import isprime from sympy import prime def a(n): for k in range(1,10**8): if isprime(prime(k)*10**n-1) and isprime(prime(k)*10**n-3) and isprime(prime(k)*10**n-7) and isprime(prime(k)*10**n-9): return prime(k) n = 1 while n < 100: print(a(n),end=', ') n+=1