Prime p₀= 2862558855900990689 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 166 2 40 2 4 2 370 2 88 2 (?)
a_n: 0 2 42 44 210 212 252 254 258 260 630 632 720 722
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: 722
Found by: JayPi
db: batch=82, k=14, 40 166 40 4 370 88

SPT(16)	2862558100837945751	0 26 38 48 80 86 90 98 120 128 132 138 170 180 192 218	-755063044938
SPT(16)	2862558130742965723	0 18 54 90 126 160 168 208 216 256 264 298 334 370 406 424	-725158024966
SPT(16)	2862558346589437303	0 84 100 108 136 150 156 190 294 328 334 348 376 384 400 484	-509311553386
SPT(16)	2862558646042149673	0 58 76 84 126 154 178 190 204 216 240 268 310 318 336 394	-209858841016
STPT(10)	2862558729965216309	0 2 18 20 30 32 42 44 60 62	-125935774380
SPT(16)	2862558773767689929	0 30 38 48 78 102 128 140 150 162 188 212 242 252 260 290	-82133300760
STPT(10)	2862559092455983379	0 2 18 20 30 32 42 44 60 62	236554992690
STPT(10)	2862559161090905399	0 2 12 14 30 32 48 50 60 62	305189914710
STPT(10)	2862559433047747787	0 2 54 56 72 74 90 92 144 146	577146757098
SPT(16)	2862559676219502289	0 64 90 118 148 154 174 232 240 298 318 324 354 382 408 472	820318511600
SPT(16)	2862560017809181793	0 48 108 120 140 158 174 228 266 320 336 354 374 386 446 494	1161908191104