Prime p₀= 2506539349082466611 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 28 2 46 2 16 2 58 2 22 2 (?)
a_n: 0 2 60 62 90 92 138 140 156 158 216 218 240 242
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: 242
Found by: [AF>Linux]Rogue 9
db: batch=82, k=14, 58 28 46 16 58 22

SPT(16)	2506538039729397599	0 24 38 50 98 104 134 158 300 324 354 360 408 420 434 458	-1309353069012
SPT(16)	2506538157050083237	0 6 42 60 70 76 102 124 132 154 180 186 196 214 250 256	-1192032383374
SPT(16)	2506538174925822901	0 66 78 100 138 190 216 240 328 352 378 430 468 490 502 568	-1174156643710
TPT(14)	2506538521990338839	0 2 12 14 78 80 120 122 132 134 150 152 210 212	-827092127772
SPT(16)	2506538522827490413	0 28 34 94 136 150 166 238 246 318 334 348 390 450 456 484	-826254976198
STPT(10)	2506539179329565201	0 2 6 8 48 50 90 92 96 98	-169752901410
STPT(12)	2506539353949878381	0 2 66 68 180 182 276 278 390 392 456 458	4867411770
STPT(10)	2506539705139226891	0 2 36 38 78 80 120 122 156 158	356056760280
TPT(14)	2506539722781294581	0 2 6 8 36 38 66 68 78 80 96 98 108 110	373698827970
STPT(10)	2506539841527727007	0 2 30 32 60 62 90 92 120 122	492445260396
STPT(10)	2506539924636789887	0 2 24 26 42 44 60 62 84 86	575554323276