Prime p₀= 2388025990740872819 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 70 2 34 2 40 2 40 2 46 2 10 2 (?)
a_n: 0 2 72 74 108 110 150 152 192 194 240 242 252 254
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=81, k=14, 70 34 40 40 46 10

SPT(18)	2388024417944699579	0 8 12 38 80 104 108 122 134 168 180 194 198 222 264 290 294 302	-1572796173240
STPT(10)	2388024466409298329	0 2 18 20 30 32 42 44 60 62	-1524331574490
SPT(16)	2388024509267281099	0 24 138 160 222 250 262 288 334 360 372 400 462 484 598 622	-1481473591720
SPT(16)	2388024789123917789	0 14 48 60 72 74 84 104 108 128 138 140 152 164 198 212	-1201616955030
SPT(16)	2388024883607451727	0 46 52 60 70 114 210 256 300 346 442 486 496 504 510 556	-1107133421092
SPT(16)	2388025455000775489	0 42 60 78 118 148 250 268 312 330 432 462 502 520 538 580	-535740097330
SPT(16)	2388025992188581037	0 24 54 56 62 140 182 200 216 234 276 354 360 362 392 416	1447708218
STPT(10)	2388025995845918609	0 2 18 20 30 32 42 44 60 62	5105045790
SPT(16)	2388026057371874581	0 76 88 138 148 162 168 172 246 250 256 270 280 330 342 418	66631001762
SPT(16)	2388026065534951097	0 6 14 20 26 54 60 84 152 176 182 210 216 222 230 236	74794078278
STPT(12)	2388026805098910089	0 2 30 32 72 74 90 92 132 134 162 164	814358037270