Prime p₀= 1956619245402988007 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 82 2 88 2 64 2 58 2 10 2 (?)
a_n: 0 2 30 32 114 116 204 206 270 272 330 332 342 344
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: 344
Found by: gemini8
db: batch=80, k=14, 28 82 88 64 58 10

SPT(16)	1956617649902783897	0 14 50 74 80 86 102 110 126 134 150 156 162 186 222 236	-1595500204110
SPT(18)	1956617805722542289	0 38 42 60 78 98 122 188 192 200 204 270 294 314 332 350 354 392	-1439680445718
SPT(16)	1956618399205642969	0 12 18 24 60 70 84 124 198 238 252 262 298 304 310 322	-846197345038
SPT(16)	1956618859387406663	0 14 18 38 56 66 74 108 116 150 158 168 186 206 210 224	-386015581344
STPT(10)	1956619045381418357	0 2 30 32 60 62 90 92 120 122	-200021569650
SPT(16)	1956619215921741577	0 6 22 42 52 76 100 156 160 216 240 264 274 294 310 316	-29481246430
STPT(10)	1956619321922001197	0 2 24 26 42 44 60 62 84 86	76519013190
SPT(16)	1956619844494539503	0 6 30 56 104 170 174 180 200 206 210 276 324 350 374 380	599091551496
SPT(16)	1956620055681144467	0 12 14 66 132 144 150 162 164 176 182 194 260 312 314 326	810278156460
SPT(16)	1956620154886068569	0 8 18 74 120 128 164 200 258 294 330 338 384 440 450 458	909483080562
STPT(10)	1956620595692367959	0 2 12 14 90 92 168 170 180 182	1350289379952