Prime p₀= 2313340821463357337 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 70 2 28 2 118 2 16 2 10 2 (?)
a_n: 0 2 12 14 84 86 114 116 234 236 252 254 264 266
All 14 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 266
Found by: WTBroughton
db: batch=81, k=14, 10 70 28 118 16 10

SPT(16)	2313340397413245157	0 60 84 100 130 174 180 192 244 256 262 306 336 352 376 436	-424050112180
SPT(16)	2313340408011240709	0 22 24 52 72 82 84 142 162 220 222 232 252 280 282 304	-413452116628
TPT(14)	2313340422717736829	0 2 30 32 42 44 72 74 132 134 138 140 258 260	-398745620508
SPT(16)	2313340455030127969	0 138 168 220 228 250 288 294 298 304 342 364 372 424 454 592	-366433229368
SPT(16)	2313340516748926631	0 18 30 42 102 116 156 182 186 212 252 266 326 338 350 368	-304714430706
SPT(16)	2313340737843342451	0 10 30 48 52 76 90 118 150 178 192 216 220 238 258 268	-83620014886
TPT(14)	2313340910497640867	0 2 30 32 42 44 72 74 252 254 264 266 384 386	89034283530
STPT(10)	2313341096415932909	0 2 18 20 30 32 42 44 60 62	274952575572
SPT(16)	2313341467979646919	0 22 28 40 42 72 84 114 148 178 190 220 222 234 240 262	646516289582
STPT(10)	2313342334988486741	0 2 36 38 78 80 120 122 156 158	1513525129404
STPT(10)	2313342407521208981	0 2 30 32 78 80 126 128 156 158	1586057851644