OFFSET
1,1
COMMENTS
All first differences except for 82799 - 2 = 82797 are multiples of 22.
EXAMPLE
The four consecutive primes {82799, 82811, 82813, 82837} are congruent to {2, 3, 5, 7} (mod 11).
MAPLE
R:= 2: count:= 1:
for p from 13 by 22 while count < 37 do
if not isprime(p) then next fi;
q:= nextprime(p); if q mod 11 <> 3 then next fi;
q:= nextprime(q); if q mod 11 <> 5 then next fi;
q:= nextprime(q); if q mod 11 = 7 then
count:= count+1; R:= R, p fi
od:
R; # Robert Israel, Sep 14 2022
MATHEMATICA
s = {2}; p1=7; Do[p1 = NextPrime[p1]; p2 = NextPrime[p1]; p3 = NextPrime[p2]; p4 = NextPrime[p3]; If[{2, 3, 5, 7} == Mod[{p1, p2, p3, p4}, 11], AppendTo[s, p1]], {10^6}]; s
CROSSREFS
KEYWORD
nonn
AUTHOR
Zak Seidov, Sep 09 2022
STATUS
approved