A390189 Primes k such that k-2 is a semiprime and k+2 is the product of 4 consecutive primes.

5003, 573888759105029, 1809317646190391, 14376723696134348849, 25250290084891174451, 41467168357376385929, 52808790448671579041, 100056004179342377939, 123142007563978632191, 351776781373081848389, 354264642484240397939, 408813360582819254399

Offset

1,1

Links

Table of n, a(n) for n=1..12.

Example

The first triplet:
  5001 = 3 * 1667
  5003 is prime
  5005 = 5 * 7 * 11 * 13
The second triplet:
  573888759105027 = 3 * 191296253035009
  573888759105029 is prime
  573888759105031 = 4877 * 4889 * 4903 * 4909
The following case is more interesting:
  100056004179342377935 = 5 * 20011200835868475587
  100056004179342377937 = 3 * 33352001393114125979
  100056004179342377939 is prime
  100056004179342377941 = 99991 * 100003 * 100019 * 100043
  100056004179342377943 = 3 * 7 * 1198651 * 3974944856833

Prog

(PARI) a390189(nterms) = my(n=0, p1=2, p2=3, p3=5); forprime(p4=7, oo, my(pp=p1*p2*p3*p4); if(ispseudoprime(pp-2) && bigomega(pp-4)==2, n++; if(n>nterms, break); print1(pp-2, ", ")); p1=p2; p2=p3; p3=p4) \\ Hugo Pfoertner, Jan 06 2026

Crossrefs

Cf. A001358, A046302.

Sequence in context: A035787 A108011 A018188 * A280879 A067226 A249081

Adjacent sequences: A390186 A390187 A390188 * A390190 A390191 A390192

Keyword

nonn

Author

Soko Kosaka, Jan 05 2026

Status

approved