A266961
Initial members of two prime quadruple pairs (A059925) with the smallest possible difference of 420.
Original entry on oeis.org
11281963036964038421, 12114914563464663491, 28316206187385412991, 52124021311991227601, 55545706433252188001, 111634607435934869981, 507606513146890423961, 530175308664549244391, 635491296817562023841, 730968587426043396971, 768781285931309901791, 780090878823500745041
Offset: 1
A256842
Initial members of 5 twin primes with the smallest possible difference of 30.
Original entry on oeis.org
39713433671, 66419473031, 71525244611, 286371985811, 480612532451, 535181743301, 789972743471, 1195575264641, 1219449947921, 1256522812841, 1292207447351, 1351477467251, 1450982599271, 1460592638171, 1515361442261, 1592346154541
Offset: 1
A213904
a(n) is the initial member of the least pair of prime quadruples (of the form p, p+2, p+6, p+8) with a difference of 30*n, with no other prime quadruple between the pair.
Original entry on oeis.org
1006301, 0, 11, 1022381, 0, 3512051, 1871, 632081, 0, 1121831, 15731, 0, 1481, 1155611, 1068251, 0, 18911, 284741, 0, 12390011, 191, 821, 0, 3837131, 875261, 0, 854921, 10865291, 18041, 0, 958541, 680291, 0, 299471, 1063961, 663581, 0, 165701
Offset: 1
For n=3, a(3)=11, since 11, 13, 17, 19 is a prime quadruple. The next prime quadruple is 101, 103, 107, 109. The difference 101-11=90, which is equal to 30*3.
A338866
Number of twins of prime quadruples < 10^n.
Original entry on oeis.org
0, 0, 0, 0, 0, 0, 4, 5, 18, 65, 267, 1238, 6196, 33480, 187932, 1095882, 6629232
Offset: 1
For n=7 the a(7)=4 solutions are: [(1006301, 1006303, 1006307, 1006309), (1006331, 1006333, 1006337, 1006339)], [(2594951, 2594953, 2594957, 2594959), (2594981, 2594983, 2594987, 2594989)], [(3919211, 3919213, 3919217, 3919219), (3919241, 3919243, 3919247, 3919249)], [(9600551, 9600553, 9600557, 9600559), (9600581, 9600583, 9600587, 9600589)].
A379677
Numbers k for which 10k+1, 10k+3, 10k+7, 10k+9, 10k+31, 10k+33, 10k+37, and 10k+39 are primes.
Original entry on oeis.org
100630, 259495, 391921, 960055, 1053106, 10881631, 13144570, 15237073, 15713164, 17902876, 21195025, 25535221, 26758786, 55745863, 68512435, 72449137, 82135765, 87141136, 103026208, 110310436, 128216002, 138120127, 142769863, 143237995, 144399400, 159672133, 194876008
Offset: 1
a(1) = 100630 since 1006301, 1006303, 1006307, 1006309, 1006331, 1006333, 1006337, and 1006339 are all prime and there are no smaller minimally close prime decades.
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from itertools import count
from sympy import isprime
def generate_a() :
for k in count() :
for j in (1,3,7,9,31,33,37,39) :
if not isprime(10*k+j) : break
else:
yield k
A382970
Numbers k such that {k, k+2, k+6, k+8, k+90, k+92, k+96, k+98} are all prime.
Original entry on oeis.org
11, 101, 15641, 3512981, 6655541, 20769311, 26919791, 41487071, 71541641, 160471601, 189425981, 236531921, 338030591, 409952351, 423685721, 431343461, 518137091, 543062621, 588273221, 637272191, 639387311, 647851571, 705497951, 726391571, 843404201, 895161341, 958438751, 960813851, 964812461, 985123961
Offset: 1
a(1) corresponds to the set of primes {11,13,17,19,101,103,107,109} and a(2) corresponds to {101,103,107,109,191,193,197,199}.
Showing 1-6 of 6 results.
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