Prime p₀= 950568262839368687 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 88 2 28 2 10 2 46 2 40 2 28 2 (?)
a_n: 0 2 90 92 120 122 132 134 180 182 222 224 252 254
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: 254
Found by: stoneageman
db: batch=76, k=14, 88 28 10 46 40 28

SPT(16)	950567302375893161	0 32 36 38 66 78 92 98 180 186 200 212 240 242 246 278	-960463475526
TPT(14)	950567454172889207	0 2 72 74 90 92 222 224 252 254 270 272 282 284	-808666479480
SPT(16)	950567536579935397	0 54 82 114 144 162 166 232 264 330 334 352 382 414 442 496	-726259433290
SPT(16)	950567977726554757	0 10 36 76 150 162 196 204 232 240 274 286 360 400 426 436	-285112813930
STPT(10)	950568044525745551	0 2 6 8 48 50 90 92 96 98	-218313623136
STPT(10)	950568079508137631	0 2 30 32 78 80 126 128 156 158	-183331231056
SPT(16)	950568489867499483	0 16 30 36 114 148 156 166 168 178 186 220 298 304 318 334	227028130796
STPT(10)	950568578271530807	0 2 30 32 42 44 54 56 84 86	315432162120
STPT(10)	950568827876397137	0 2 42 44 72 74 102 104 144 146	565037028450
STPT(10)	950569077529803617	0 2 54 56 72 74 90 92 144 146	814690434930
SPT(16)	950569330025877911	0 12 18 32 56 60 66 152 156 242 248 252 276 290 296 308	1067186509224