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Revision History for A364778

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A364778

Products of two distinct strong primes.
(history; published version)

#10 by N. J. A. Sloane at Sun Oct 08 09:45:46 EDT 2023

STATUS

editing

approved

#9 by N. J. A. Sloane at Sun Oct 08 09:45:43 EDT 2023

NAME

Semiprimes (products Products of two primes) whose factors are distinct strong primes.

CROSSREFS

Cf. A001358, A051634, A363167, A363782.

EXTENSIONS

Definition clarified by N. J. A. Sloane, Oct 08 2023

STATUS

approved

editing

#8 by N. J. A. Sloane at Wed Sep 06 21:13:38 EDT 2023

STATUS

proposed

approved

#7 by Andrew Howroyd at Sun Aug 13 22:39:16 EDT 2023

STATUS

editing

proposed

#6 by Andrew Howroyd at Sun Aug 13 22:38:47 EDT 2023

CROSSREFS

Cf. A001358, A051634, A363782.

STATUS

proposed

editing

Discussion

Sun Aug 13

22:39

Andrew Howroyd: So could be crossref.

#5 by Amiram Eldar at Mon Aug 07 02:32:39 EDT 2023

STATUS

editing

proposed

#4 by Amiram Eldar at Mon Aug 07 02:32:31 EDT 2023

NAME

Semiprimes (products of two primes) whose factors are strong primes.

MATHEMATICA

strongQ[p_] := p > 2 && 2*p > Total[NextPrime[p, {-1, 1}]]; Select[Range[1, 3000, 2], MemberQ[{{1, 1}, {2}}, (f = FactorInteger[#])[[;; , 2]]] && AllTrue[f[[;; , 1]], strongQ] &] (* Amiram Eldar, Aug 07 2023 *)

STATUS

proposed

editing

#3 by Massimo Kofler at Mon Aug 07 02:11:51 EDT 2023

STATUS

editing

proposed

#2 by Massimo Kofler at Mon Aug 07 02:10:47 EDT 2023

NAME

allocated for Massimo Kofler Semiprimes (products of two primes) whose factors are strong primes.

DATA

121, 187, 289, 319, 407, 451, 493, 629, 649, 697, 737, 781, 841, 869, 1003, 1067, 1073, 1111, 1139, 1177, 1189, 1207, 1343, 1369, 1397, 1507, 1517, 1639, 1649, 1681, 1711, 1717, 1793, 1819, 1943, 1969, 2059, 2101, 2159, 2167, 2183, 2291, 2329, 2419, 2453, 2479, 2497, 2533, 2627, 2629, 2747

OFFSET

1,1

COMMENTS

Strong primes: prime(n) > (prime(n-1) + prime(n+1))/2.

EXAMPLE

121 = 11^2 and 11 > (7+13)/2.

187 = 11*17 and 11 > (7+13)/2, 17 > (13+19)/2.

493 = 17*29 and 17 > (13+19)/2, 29 > (23+31)/2.

CROSSREFS

Cf. A001358, A051634.

KEYWORD

allocated

nonn

AUTHOR

Massimo Kofler, Aug 07 2023

STATUS

approved

editing

Discussion

Mon Aug 07

02:11

Massimo Kofler: Sphenics (products of three distinct primes) whose factors are strong primes are in A363782.

#1 by Massimo Kofler at Mon Aug 07 02:10:47 EDT 2023

NAME

allocated for Massimo Kofler

KEYWORD

allocated

STATUS

approved