Prime p₀= 2537568523278488459 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 46 2 88 2 40 2 40 2 46 2 10 2 (?)
a_n: 0 2 48 50 138 140 180 182 222 224 270 272 282 284
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: 284
Found by: RFGuy_KCCO
db: batch=82, k=14, 46 88 40 40 46 10

SPT(16)	2537567049657164251	0 42 46 48 72 112 126 156 172 202 216 256 280 282 286 328	-1473621324208
SPT(16)	2537567205989871997	0 22 60 64 102 120 126 132 184 190 196 214 252 256 294 316	-1317288616462
STPT(10)	2537567340584668307	0 2 24 26 42 44 60 62 84 86	-1182693820152
SPT(16)	2537567851491622151	0 30 42 68 90 108 168 170 210 212 272 290 312 338 350 380	-671786866308
STPT(10)	2537568274860663227	0 2 30 32 42 44 54 56 84 86	-248417825232
SPT(16)	2537568453114664777	0 12 66 96 112 136 150 156 190 196 210 234 250 280 334 346	-70163823682
SPT(20)	2537568617826567779	0 2 44 60 68 72 150 168 180 194 198 212 224 242 320 324 332 348 390 392	94548079320
SPT(16)	2537569295029732127	0 2 20 54 72 90 164 182 222 240 314 332 350 384 402 404	771751243668
TPT(14)	2537569317222555527	0 2 30 32 72 74 90 92 162 164 174 176 240 242	793944067068
STPT(10)	2537569334247753101	0 2 6 8 18 20 30 32 36 38	810969264642
STPT(10)	2537569396816011287	0 2 30 32 72 74 114 116 144 146	873537522828