A079020 Suppose p and q = p+20 are primes. Define the difference pattern of (p,q) to be the successive differences of the primes in the range p to q. There are 56 possible difference patterns, shown in the Comments line. Sequence gives smallest value of p for each difference pattern, sorted by magnitude.

3, 11, 17, 23, 41, 47, 59, 83, 89, 107, 131, 137, 179, 191, 251, 293, 317, 347, 353, 359, 389, 401, 467, 503, 521, 593, 599, 653, 887, 947, 971, 1031, 1151, 1193, 1229, 1259, 1301, 1307, 1439, 1601, 1931, 1979, 1997, 2069, 2531, 3167, 3299, 4241, 5261, 5639, 5849, 8081, 10091, 17189, 18041, 19421

Offset: 1

Author

Labos Elemer, Jan 24 2003

Keywords

• fini
• full
• nonn

Comments

The 56 difference patterns are [20], [2,18], [6,14], [8,12], [12,8], [14,6], [18,2], [2,4,14], [2,6,12], [2,10,8], [2,12,6], [2,16,2], [6,2,12], [6,6,8], [6,8,6], [6,12,2], [8,4,8], [8,6,6], [8,10,2], [12,2,6], [12,6,2], [14,4,2], [2,4,2,12], [2,4,6,8], [2,4,8,6], [2,4,12,2], [2,6,4,8], [2,6,6,6], [2,6,10,2], [2,10,2,6], [2,10,6,2], [2,12,4,2], [6,2,4,8], [6,2,6,6], [6,2,10,2], [6,6,2,6], [6,6,6,2], [6,8,4,2], [8,4,2,6], [8,4,6,2], [8,6,4,2], [12,2,4,2], [2,4,2,4,8], [2,4,2,10,2], [2,4,6,2,6], [2,4,6,6,2], [2,6,4,2,6], [2,6,4,6,2], [2,6,6,4,2], [2,10,2,4,2], [6,2,4,6,2], [6,2,6,4,2], [8,4,2,4,2], [2,4,2,4,6,2], [2,6,4,2,4,2], [2,2,4,2,4,2,4].

Certain patterns are singular, i.e. occur only once like [2,2,4,2,4,2,4]. Impossible patterns are [2,14,4] or [10,10] etc.

Examples

			p=10091, q=10111 has difference pattern [2, 6, 4, 8] and {10091, 10093, 10099, 10103, 10111} is the corresponding consecutive prime 5-tuple.
		

Crossrefs

A000230(10)=A031938(1)=887, A078951(1)=3299, A078965(1)=47, A078968(1)=251.

Cf. A079016-A079024.

Extensions

Edited by Rick L. Shepherd, Sep 10 2003