Prime p₀= 2366915364525289559 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 46 2 40 2 28 2 130 2 4 2 148 2 (?)
a_n: 0 2 48 50 90 92 120 122 252 254 258 260 408 410
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: 410
Found by: Landjunge
db: batch=81, k=14, 46 40 28 130 4 148

SPT(16)	2366913625780626749	0 12 78 84 110 180 198 234 308 344 362 432 458 464 530 542	-1738744662810
SPT(16)	2366913767491724489	0 54 104 110 192 210 260 272 282 294 344 362 444 450 500 554	-1597033565070
TPT(14)	2366914081419767729	0 2 42 44 48 50 90 92 150 152 180 182 252 254	-1283105521830
SPT(16)	2366914087549317437	0 50 102 150 192 224 234 242 252 260 270 302 344 392 444 494	-1276975972122
SPT(16)	2366914602191111569	0 24 42 48 88 102 114 130 132 148 160 174 214 220 238 262	-762334177990
SPT(16)	2366914717763653219	0 52 60 142 198 208 220 232 270 282 294 304 360 442 450 502	-646761636340
STPT(10)	2366915521834158401	0 2 30 32 120 122 210 212 240 242	157308868842
SPT(16)	2366915607043574989	0 12 28 72 100 138 168 178 294 304 334 372 400 444 460 472	242518285430
TPT(14)	2366915653933985249	0 2 12 14 138 140 210 212 240 242 252 254 270 272	289408695690
STPT(10)	2366915828331097331	0 2 36 38 78 80 120 122 156 158	463805807772
STPT(10)	2366915845831197641	0 2 30 32 78 80 126 128 156 158	481305908082