Prime p₀= 2956851501571835669 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 46 2 88 2 28 2 10 2 16 2 70 2 (?)
a_n: 0 2 48 50 138 140 168 170 180 182 198 200 270 272
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: 272
Found by: Asgard2022
db: batch=82, k=14, 46 88 28 10 16 70

SPT(16)	2956848800927852683	0 40 76 130 178 208 238 250 264 276 306 336 384 438 474 514	-2700643982986
SPT(16)	2956849055166172931	0 20 30 32 36 42 98 102 146 150 206 212 216 218 228 248	-2446405662738
SPT(16)	2956849668950630861	0 18 36 66 78 92 122 150 308 336 366 380 392 422 440 458	-1832621204808
SPT(16)	2956850748874005337	0 84 90 96 120 124 144 162 214 232 252 256 280 286 292 376	-752697830332
SPT(16)	2956851095799174853	0 6 34 60 76 136 156 214 240 298 318 378 394 420 448 454	-405772660816
SPT(16)	2956851299549482079	0 50 54 62 78 122 132 138 164 170 180 224 240 248 252 302	-202022353590
STPT(12)	2956851599335604039	0 2 42 44 102 104 108 110 168 170 210 212	97763768370
SPT(16)	2956851950571007421	0 30 38 48 98 116 150 168 188 206 240 258 308 318 326 356	448999171752
SPT(16)	2956853052854240821	0 22 58 106 112 120 172 190 228 246 298 306 312 360 396 418	1551282405152
STPT(12)	2956853193504950417	0 2 12 14 30 32 42 44 60 62 72 74	1691933114748
STPT(10)	2956853899764907691	0 2 6 8 48 50 90 92 96 98	2398193072022