Prime p₀= 1458796343573522909 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 16 2 40 2 34 2 40 2 16 2 (?)
a_n: 0 2 42 44 60 62 102 104 138 140 180 182 198 200
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: 200
Found by: MarkRBright
db: batch=78, k=14, 40 16 40 34 40 16

SPT(16)	1458795095138414773	0 4 6 10 24 36 46 84 130 168 178 190 204 208 210 214	-1248435108136
STPT(10)	1458795184863410477	0 2 30 32 72 74 114 116 144 146	-1158710112432
STPT(10)	1458795896903648267	0 2 30 32 42 44 54 56 84 86	-446669874642
STPT(10)	1458795904634282057	0 2 30 32 42 44 54 56 84 86	-438939240852
SPT(16)	1458796203199160377	0 12 34 40 52 54 90 94 210 214 250 252 264 270 292 304	-140374362532
SPT(16)	1458796286081880247	0 6 10 24 34 64 76 94 102 120 132 162 172 186 190 196	-57491642662
STPT(12)	1458796343573522951	0 2 18 20 60 62 96 98 138 140 156 158	42
SPT(16)	1458796467177170783	0 54 60 90 134 138 194 198 200 204 260 264 308 338 344 398	123603647874
SPT(16)	1458796489936178867	0 60 66 74 152 174 180 194 222 236 242 264 342 350 356 416	146362655958
STPT(10)	1458797418773778287	0 2 12 14 42 44 72 74 84 86	1075200255378
SPT(16)	1458798168532953253	0 4 10 48 66 106 144 178 186 220 258 298 316 354 360 364	1824959430344