Prime p₀= 2379146686609254167 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 82 2 46 2 10 2 34 2 58 2 22 2 (?)
a_n: 0 2 84 86 132 134 144 146 180 182 240 242 264 266
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: Landjunge
db: batch=81, k=14, 82 46 10 34 58 22

STPT(10)	2379146050491804071	0 2 30 32 78 80 126 128 156 158	-636117450096
STPT(10)	2379146085185914727	0 2 12 14 72 74 132 134 144 146	-601423339440
SPT(16)	2379146577093636173	0 6 20 26 48 54 80 84 200 204 230 236 258 264 278 284	-109515617994
SPT(16)	2379146643945507463	0 10 54 88 130 136 144 154 240 250 258 264 306 340 384 394	-42663746704
STPT(10)	2379146648767073369	0 2 30 32 60 62 90 92 120 122	-37842180798
SPT(16)	2379146652436173187	0 24 42 66 72 84 240 280 306 346 502 514 520 544 562 586	-34173080980
STPT(10)	2379147583920798149	0 2 18 20 30 32 42 44 60 62	897311543982
STPT(10)	2379147928014807359	0 2 48 50 90 92 132 134 180 182	1241405553192
STPT(10)	2379148637464939511	0 2 96 98 108 110 120 122 216 218	1950855685344
SPT(16)	2379149386265416519	0 40 102 124 208 240 244 258 304 318 322 354 438 460 522 562	2699656162352
TPT(14)	2379149453368021457	0 2 12 14 54 56 60 62 90 92 144 146 180 182	2766758767290