Prime p₀= 2377768750216833221 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 76 2 40 2 16 2 70 2 76 2 46 2 (?)
a_n: 0 2 78 80 120 122 138 140 210 212 288 290 336 338
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: 338
Found by: [SG-2W]Kurzer
db: batch=81, k=14, 76 40 16 70 76 46

SPT(16)	2377767387134952017	0 2 6 20 32 44 62 66 140 144 162 174 186 200 204 206	-1363081881204
SPT(16)	2377767504739378673	0 8 36 108 138 206 234 264 290 320 348 416 446 518 546 554	-1245477454548
SPT(16)	2377767625830421777	0 30 36 40 42 82 84 96 130 142 144 184 186 190 196 226	-1124386411444
SPT(16)	2377768204781532841	0 12 18 36 102 106 130 148 150 168 192 196 262 280 286 298	-545435300380
SPT(16)	2377768258541961713	0 26 44 50 54 86 96 126 164 194 204 236 240 246 264 290	-491674871508
STPT(10)	2377768496906505551	0 2 36 38 78 80 120 122 156 158	-253310327670
STPT(10)	2377768944489218279	0 2 18 20 30 32 42 44 60 62	194272385058
STPT(10)	2377768995335847401	0 2 120 122 138 140 156 158 276 278	245119014180
SPT(18)	2377769074340986549	0 10 28 34 42 60 88 94 178 234 318 324 352 370 378 384 402 412	324124153328
SPT(16)	2377769793356580683	0 8 54 56 78 90 98 110 114 126 134 146 168 170 216 224	1043139747462
STPT(10)	2377770081119289299	0 2 42 44 60 62 78 80 120 122	1330902456078