Prime p₀= 4503844164310582127 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 22 2 88 2 76 2 46 2 10 2 10 2 (?)
a_n: 0 2 24 26 114 116 192 194 240 242 252 254 264 266
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: 266
Found by: Antares2022
db: batch=85, k=14, 22 88 76 46 10 10

SPT(16)	4503842532427697299	0 10 24 60 102 154 162 210 232 280 288 340 382 418 432 442	-1631882884828
SPT(16)	4503842786720686027	0 16 22 82 160 204 216 262 264 310 322 366 444 504 510 526	-1377589896100
SPT(16)	4503843149064965023	0 6 30 54 58 66 106 120 154 168 208 216 220 244 268 274	-1015245617104
SPT(16)	4503843247508678869	0 108 112 120 210 274 288 294 358 364 378 442 532 540 544 652	-916801903258
SPT(16)	4503843356063592817	0 12 16 30 64 126 136 150 196 210 220 282 316 330 334 346	-808246989310
STPT(10)	4503844098276271919	0 2 18 20 30 32 42 44 60 62	-66034310208
SPT(16)	4503844217849316727	0 6 52 100 114 142 160 162 184 186 204 232 246 294 340 346	53538734600
SPT(16)	4503844457109749677	0 16 30 46 60 72 142 156 190 204 274 286 300 316 330 346	292799167550
SPT(16)	4503844460252417729	0 14 54 72 102 108 120 138 224 242 254 260 290 308 348 362	295941835602
STPT(10)	4503844485865055657	0 2 30 32 42 44 54 56 84 86	321554473530
STPT(10)	4503844495745264237	0 2 12 14 42 44 72 74 84 86	331434682110