A064432
Least k such that k*10^n-9, k*10^n-7, k*10^n-3 and k*10^n-1 are all prime.
Original entry on oeis.org
14, 2, 2, 248, 1856, 7190, 719, 15308, 13415, 18434, 13532, 26975, 6935, 61763, 17786, 60140, 6014, 297974, 103199, 56321, 80009, 428186, 303476, 32558, 1361063, 444275, 634451, 116573, 303593, 293822, 1068491, 651464, 1855937, 3217754, 364985, 569129
Offset: 0
a(1) = 2 because 19, 17, 13 and 11 are all prime.
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Do[k = 1; While[ !PrimeQ[k*10^n - 1] || !PrimeQ[k*10^n - 3] || !PrimeQ[k*10^n - 7] || !PrimeQ[k*10^n - 9], k++ ]; Print[k], {n, 0, 35} ] (* Robert G. Wilson v *)
A121066
Least positive k such that 10^n + {k, k+2, k+6, k+8} are all prime.
Original entry on oeis.org
4, 1, 1, 481, 3001, 1111, 2341, 13951, 5461, 25261, 57421, 7531, 123691, 56581, 945721, 67441, 1346491, 325231, 430711, 2139271, 2561161, 81721, 4319041, 571381, 4331251, 1232251, 7114471, 3185011, 407581, 1500631, 1846021, 1346611
Offset: 0
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A[0]:= 4:
for n from 1 to 30 do
for k from 1 by 30 do
if andmap(isprime, map(`+`,[0,2,6,8],10^n+k)) then
A[n]:= k; break
fi;
od od:
seq(A[n],n=0..30); # Robert Israel, May 06 2015
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lpk[n_]:=Module[{k=1,x=10^n},While[AnyTrue[x+ k+{0,2,6,8}, CompositeQ], k++];k]; Table[lpk[n],{n,0,15}] (* The program generates the first 16 terms of the sequence. *) (* Harvey P. Dale, Jun 18 2022 *)
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print1(4,", "); n=0; until(n==100, n++; x=1; y=0; until(y==1, if(isprime(10^n+x), if(isprime(10^n+x+2), if(isprime(10^n+x+6), if(isprime(10^n+x+8), y++, x=x+30), x=x+30), x=x+30), x=x+30); if(y==1, print1(x,", ")))) \\ Tim Johannes Ohrtmann, May 04 2015
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a(n)=if(n==0, return(4)); my(k=10^n+1); while(!isprime(k) || !isprime(k+2) || !isprime(k+6) || !isprime(k+8), k+=30); k-10^n \\ Charles R Greathouse IV, May 06 2015
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.
Original entry on oeis.org
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
Offset: 1
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.
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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 *)
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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
Showing 1-3 of 3 results.
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