A274527 Prime numbers p such that p+2, p^2+p-1, p^2+p+1, p^2+3*p+1, p^2+3*p+3 are all prime numbers.

5, 2729, 26449079, 27188279, 44521679, 46090379, 52736249, 62320439, 70777979, 92520539, 109505969, 192153149, 274448789, 288269519, 343801919, 359240069, 515694899, 521594639, 527159429, 660223409, 809600819, 857353139, 921868289, 945420629, 1000777049

Offset

1,1

Links

Pierre CAMI, Table of n, a(n) for n = 1..45

Example

2 first prime, 2+2=4 composite.
3 prime, 3+2=5 prime, 3^2+3-1=11 prime, 3^2+3+1=13 prime, 3^2+3*3+1=19 prime, 3^2+3*3+3=21 composite.
5 prime, 5+2=7 prime, 5^2+5-1=29 prime, 5^2+5+1=31 prime, 5^2+3*5+1=41 prime, 5^2+3*5+3=43 prime so a(1)=5

Mathematica

Select[Prime[Range[50890000]], AllTrue[{#+2, #^2+#-1, #^2+#+1, #^2+3#+1, #^2+3#+3}, PrimeQ]&] (* Harvey P. Dale, Aug 13 2021 *)

Prog

(PFGW & SCRIPT)
twin.txt file with the smallest of twin pairs.
SCRIPT
DIM m
DIM n
OPENFILEIN maf, twin.txt
OPENFILEOUT myf, a.txt
LABEL loop
GETNEXT n, maf
SET m, n*(n+1)-1
PRP m
IF ISPRP THEN GOTO a
GOTO loop
LABEL a
PRP m+2
IF ISPRP THEN GOTO b
GOTO loop
LABEL b
SET n, n+2
SET m, n*(n-1)-1
PRP m
IF ISPRP THEN GOTO c
GOTO loop
LABEL c
SET m, m+2
PRP m
SET n, n-2
IF ISPRP THEN WRITE myf, n
GOTO loop

Crossrefs

Cf. A228968, A274525.

Sequence in context: A036772 A117011 A367957 * A258980 A096934 A076912

Adjacent sequences: A274524 A274525 A274526 * A274528 A274529 A274530

Keyword

nonn

Author

Pierre CAMI, Jun 27 2016

Status

approved