Prime p₀= 3007711371700579457 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 46 2 22 2 58 2 34 2 58 2 (?)
a_n: 0 2 42 44 90 92 114 116 174 176 210 212 270 272
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: 272
Found by: Orange Kid
db: batch=82, k=14, 40 46 22 58 34 58

TPT(14)	3007711125800688407	0 2 42 44 114 116 144 146 204 206 240 242 270 272	-245899891050
SPT(16)	3007711203683304851	0 68 110 132 186 276 300 332 336 368 392 482 536 558 600 668	-168017274606
TPT(14)	3007711222644398717	0 2 42 44 54 56 72 74 234 236 252 254 264 266	-149056180740
STPT(12)	3007711222644398759	0 2 12 14 30 32 192 194 210 212 222 224	-149056180698
SPT(16)	3007711319156763641	0 38 56 60 78 86 102 108 140 146 162 170 188 192 210 248	-52543815816
STPT(10)	3007711345845030827	0 2 30 32 72 74 114 116 144 146	-25855548630
STPT(10)	3007711491639527381	0 2 36 38 78 80 120 122 156 158	119938947924
TPT(14)	3007711591462166471	0 2 36 38 78 80 120 122 126 128 150 152 156 158	219761587014
SPT(16)	3007711596076429399	0 10 28 48 58 72 108 112 198 202 238 252 262 282 300 310	224375849942
STPT(10)	3007711906714445471	0 2 30 32 78 80 126 128 156 158	535013866014
SPT(16)	3007712395756279613	0 26 108 128 138 176 240 246 350 356 420 458 468 488 570 596	1024055700156