Prime p₀= 2846580122134753049 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 148 2 154 2 52 2 64 2 28 2 (?)
a_n: 0 2 42 44 192 194 348 350 402 404 468 470 498 500
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: 500
Found by: JayPi
db: batch=82, k=14, 40 148 154 52 64 28

SPT(16)	2846578805981963813	0 14 26 36 50 80 90 104 126 140 150 180 194 204 216 230	-1316152789236
STPT(10)	2846578909197908627	0 2 30 32 42 44 54 56 84 86	-1212936844422
SPT(16)	2846579079038011921	0 6 28 42 90 108 130 132 196 198 220 238 286 300 322 328	-1043096741128
STPT(10)	2846579384358722561	0 2 6 8 48 50 90 92 96 98	-737776030488
SPT(16)	2846579671725865301	0 6 20 30 42 48 80 90 98 108 140 146 158 168 182 188	-450408887748
SPT(16)	2846579716902130169	0 42 80 90 102 104 114 132 182 200 210 212 224 234 272 314	-405232622880
TPT(14)	2846580215885292431	0 2 18 20 138 140 180 182 240 242 270 272 276 278	93750539382
SPT(16)	2846580727121769487	0 66 100 114 192 234 246 276 280 310 322 364 442 456 490 556	604987016438
SPT(16)	2846580809088718109	0 14 42 92 114 128 140 144 158 162 174 188 210 260 288 302	686953965060
STPT(10)	2846580917484354287	0 2 12 14 42 44 72 74 84 86	795349601238
STPT(10)	2846580926308804667	0 2 54 56 132 134 210 212 264 266	804174051618