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A242564 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. 1
19, 1657, 13, 9001, 283, 115201, 61507, 249439, 375127, 472831, 786823, 172489, 1237, 2359033, 163063, 961981, 1442017, 457, 1208833, 4845583, 1146877, 11550193, 436831, 1911031, 581047, 4504351, 215737, 3685051, 27805381, 1343791, 82491967, 15696349, 20446423 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
EXAMPLE
2*10^3+1 (2001), 2*10^3+3 (2003), 2*10^3+7 (2007) and 2*10^3+9 (2009) are not all prime.
3*10^3+1 (3001), 3*10^3+3 (3003), 3*10^3+7 (3007) and 3*10^3+9 (3009) are not all prime.
5*10^3+1 (5001), 5*10^3+3 (5003), 5*10^3+7 (5007) and 5*10^3+9 (5009) are not all prime.
7*10^3+1 (7001), 7*10^3+3 (7003), 7*10^3+7 (7007) and 7*10^3+9 (7009) are not all prime.
11*10^3+1 (11001), 11*10^3+3 (11003), 11*10^3+7 (11007) and 11*10^3+9 (11009) are not all prime.
13*10^3+1 (13001), 13*10^3+3 (13003), 13*10^3+7 (13007) and 13*10^3+9 (13009) are all prime. Thus, a(3) = 13.
MATHEMATICA
lpp[n_]:=Module[{c=10^n, p=2}, While[Not[AllTrue[p*c+{1, 3, 7, 9}, PrimeQ]], p= NextPrime[ p]]; p]; Array[lpp, 40] (* Harvey P. Dale, Mar 24 2018 *)
PROG
(Python)
import sympy
from sympy import isprime
from sympy import prime
def Pr(n):
..for p in range(1, 10**7):
....if isprime(prime(p)*(10**n)+1) and isprime(prime(p)*(10**n)+3) and isprime(prime(p)*(10**n)+7) and isprime(prime(p)*(10**n)+9):
......return prime(p)
n = 1
while n < 50:
..print(Pr(n))
..n += 1
CROSSREFS
Sequence in context: A223498 A352465 A054949 * A068748 A289736 A180394
KEYWORD
nonn,hard
AUTHOR
Derek Orr, May 17 2014
STATUS
approved

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Last modified July 24 15:34 EDT 2024. Contains 374584 sequences. (Running on oeis4.)