|
|
A136720
|
|
Prime quadruples: 2nd term.
|
|
3
|
|
|
7, 13, 103, 193, 823, 1483, 1873, 2083, 3253, 3463, 5653, 9433, 13003, 15643, 15733, 16063, 18043, 18913, 19423, 21013, 22273, 25303, 31723, 34843, 43783, 51343, 55333, 62983, 67213, 69493, 72223, 77263, 79693, 81043, 82723, 88813, 97843
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Primes p such that p-2, p+4, and p+6 are prime. Apart from the first term, a(n) = 13 (mod 30).
|
|
LINKS
|
|
|
FORMULA
|
|
|
EXAMPLE
|
The four terms in the first quadruple are 5,7,11,13 and in the 2nd 11,13,17,19. The four terms or members of each set must be simultaneously prime.
|
|
MAPLE
|
p2:= 0: p3:= 0: p4:= 0:
Res:= NULL: count:= 0:
while count < 100 do
p1:= p2; p2:= p3; p3:= p4;
p4:= nextprime(p4);
if [p2-p1, p3-p2, p4-p3] = [2, 4, 2] then
count:= count+1; Res:= Res, p2
fi
od:
|
|
MATHEMATICA
|
lst={}; Do[p0=Prime[n]; If[PrimeQ[p2=p0+2], If[PrimeQ[p6=p0+6], If[PrimeQ[p8=p0+8], AppendTo[lst, p2]]]], {n, 12^4}]; lst (* Vladimir Joseph Stephan Orlovsky, Aug 22 2008 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|