A104875 Semiprimes of the form prime(n)*prime(n+1)*prime(n+2)*prime(n+3)*prime(n+4) - 1.

15014, 1062346, 600662302, 2224636919002, 118335570521086, 168652154886862, 3790374062238502, 6290838589498366, 127018534712243098, 131125107904515418, 190740905520325018, 2057351971883521282, 3151949824862998762

Offset: 1

Author

Jonathan Vos Post, Mar 29 2005

Keywords

• easy
• nonn

Comments

This is the five-consecutive-prime minus one equivalent of A103533.

Examples

			n prime(n) * prime(n+1) * prime(n+2) * prime(n+3) * prime(n+4) - 1
1: 2 * 3 * 5 * 7 * 11 - 1 = 2309 is prime; examples hereafter are semiprime
2: 3 * 5 * 7 * 11 * 13 - 1 = 15014 = 2 * 7507
5: 11 * 13 * 17 * 19 * 23 - 1 = 1062346 = 2 * 531173
15: 47 * 53 * 59 * 61 * 67 - 1 = 600662302 = 2 * 300331151
60: 281 * 283 * 293 * 307 * 311 - 1 = 2224636919002 = 2 * 1112318459501
117: 643 * 647 * 653 * 659 * 661 - 1 = 118335570521086 = 2 * 59167785260543
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A001358, A006881, A103533, A103614, A103746, A104874.

Programs

Mathematica

Bigomega[n_]:=Plus@@Last/@FactorInteger[n]; SemiprimeQ[n_]:=Bigomega[n]==2; Select[Table[Prime[n]*Prime[n+1]*Prime[n+2]*Prime[n+3]*Prime[n+4]-1, {n, 1000}], SemiprimeQ] (* Ray Chandler, Mar 29 2005 *)

Extensions

Extended by Ray Chandler, Mar 29 2005