Prime p₀= 2506539722781294581 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 4 2 28 2 28 2 10 2 16 2 10 2 (?)
a_n: 0 2 6 8 36 38 66 68 78 80 96 98 108 110
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: 110
Found by: [AF>Linux]Rogue 9
db: batch=82, k=14, 4 28 28 10 16 10

TPT(14)	2506538521990338839	0 2 12 14 78 80 120 122 132 134 150 152 210 212	-1200790955742
SPT(16)	2506538522827490413	0 28 34 94 136 150 166 238 246 318 334 348 390 450 456 484	-1199953804168
STPT(10)	2506539179329565201	0 2 6 8 48 50 90 92 96 98	-543451729380
TPT(14)	2506539349082466611	0 2 60 62 90 92 138 140 156 158 216 218 240 242	-373698827970
STPT(12)	2506539353949878381	0 2 66 68 180 182 276 278 390 392 456 458	-368831416200
STPT(10)	2506539705139226891	0 2 36 38 78 80 120 122 156 158	-17642067690
STPT(10)	2506539841527727007	0 2 30 32 60 62 90 92 120 122	118746432426
STPT(10)	2506539924636789887	0 2 24 26 42 44 60 62 84 86	201855495306
SPT(16)	2506540141101501031	0 16 22 30 36 60 132 142 246 256 328 352 358 366 372 388	418320206450
SPT(16)	2506540364862678457	0 24 42 76 150 162 192 196 210 214 244 256 330 364 382 406	642081383876
TPT(14)	2506541003821440809	0 2 12 14 18 20 108 110 168 170 210 212 222 224	1281040146228