Prime p₀= 2123555601801721721 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 4 2 52 2 34 2 40 2 28 2 16 2 (?)
a_n: 0 2 6 8 60 62 96 98 138 140 168 170 186 188
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: 188
Found by: Landjunge
db: batch=80, k=14, 4 52 34 40 28 16

SPT(16)	2123553460079824159	0 24 34 70 88 118 132 160 162 190 204 234 252 288 298 322	-2141721897562
STPT(10)	2123553846793158737	0 2 60 62 72 74 84 86 144 146	-1755008562984
STPT(10)	2123554154522812181	0 2 30 32 78 80 126 128 156 158	-1447278909540
SPT(16)	2123554480894474027	0 82 96 136 142 162 180 186 190 196 214 234 240 280 294 376	-1120907247694
SPT(16)	2123554640883053207	0 60 102 146 200 242 284 294 362 372 414 456 510 554 596 656	-960918668514
SPT(16)	2123555083117448083	0 36 48 54 64 174 178 190 264 276 280 390 400 406 418 454	-518684273638
SPT(16)	2123556091849636537	0 46 52 60 66 90 126 130 132 136 172 196 202 210 216 262	490047914816
STPT(12)	2123556658849947617	0 2 30 32 90 92 114 116 174 176 204 206	1057048225896
SPT(16)	2123556673091480699	0 8 14 18 24 44 78 102 140 164 198 218 224 228 234 242	1071289758978
STPT(10)	2123556725920704407	0 2 54 56 132 134 210 212 264 266	1124118982686
SPT(16)	2123557005403436711	0 6 26 30 36 72 78 80 138 140 146 182 188 192 212 218	1403601714990