Prime p₀= 1944286638922113719 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 40 2 16 2 76 2 28 2 22 2 (?)
a_n: 0 2 60 62 102 104 120 122 198 200 228 230 252 254
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: Landjunge
db: batch=80, k=14, 58 40 16 76 28 22

SPT(16)	1944285506481075257	0 26 30 42 104 120 126 132 134 140 146 162 224 236 240 266	-1132441038462
STPT(10)	1944285892632893837	0 2 24 26 42 44 60 62 84 86	-746289219882
SPT(16)	1944285958805138329	0 40 58 72 124 154 168 198 244 274 288 318 370 384 402 442	-680116975390
STPT(10)	1944286482463991129	0 2 48 50 60 62 72 74 120 122	-156458122590
STPT(10)	1944286535484188681	0 2 36 38 78 80 120 122 156 158	-103437925038
SPT(16)	1944286581724988209	0 18 22 88 130 150 154 190 192 228 232 252 294 360 364 382	-57197125510
STPT(10)	1944287082707823107	0 2 60 62 102 104 144 146 204 206	443785709388
SPT(16)	1944287224469263501	0 16 58 88 102 106 130 142 156 168 192 196 210 240 282 298	585547149782
STPT(10)	1944287245284688781	0 2 36 38 78 80 120 122 156 158	606362575062
SPT(16)	1944288030287579027	0 20 42 44 50 72 74 86 90 102 104 126 132 134 156 176	1391365465308
SPT(16)	1944288110859198431	0 12 20 26 42 48 132 158 210 236 320 326 342 348 356 368	1471937084712