Prime p₀= 2501868524851147271 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 106 2 10 2 34 2 22 2 16 2 76 2 (?)
a_n: 0 2 108 110 120 122 156 158 180 182 198 200 276 278
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: 278
Found by: JayPi
db: batch=82, k=14, 106 10 34 22 16 76

SPT(16)	2501867673614651767	0 10 34 46 84 124 126 166 174 214 216 256 294 306 330 340	-851236495504
STPT(10)	2501867819427679397	0 2 90 92 102 104 114 116 204 206	-705423467874
STPT(10)	2501868024849600761	0 2 6 8 48 50 90 92 96 98	-500001546510
STPT(10)	2501868073778814437	0 2 54 56 72 74 90 92 144 146	-451072332834
SPT(16)	2501868371585205251	0 26 48 62 72 116 128 156 182 210 222 266 276 290 312 338	-153265942020
TPT(14)	2501868476191671239	0 2 30 32 42 44 48 50 78 80 132 134 162 164	-48659476032
STPT(10)	2501869048304582399	0 2 18 20 60 62 102 104 120 122	523453435128
STPT(10)	2501869571106349259	0 2 48 50 90 92 132 134 180 182	1046255201988
SPT(16)	2501869587995440919	0 2 12 18 42 50 60 78 92 110 120 128 152 158 168 170	1063144293648
STPT(10)	2501869829079065969	0 2 18 20 30 32 42 44 60 62	1304227918698
STPT(10)	2501870044584358697	0 2 12 14 42 44 72 74 84 86	1519733211426