Prime p₀= 2062561741406759807 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 52 2 4 2 40 2 136 2 22 2 16 2 (?)
a_n: 0 2 54 56 60 62 102 104 240 242 264 266 282 284
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: 284
Found by: Cruncher Pete
db: batch=80, k=14, 52 4 40 136 22 16

TPT(14)	2062560837066575849	0 2 42 44 78 80 90 92 132 134 150 152 168 170	-904340183958
STPT(10)	2062560860717319671	0 2 36 38 78 80 120 122 156 158	-880689440136
STPT(10)	2062561262414470427	0 2 30 32 42 44 54 56 84 86	-478992289380
SPT(16)	2062561266668803193	0 24 44 74 90 116 156 228 236 308 348 374 390 420 440 464	-474737956614
STPT(10)	2062561314327801809	0 2 18 20 30 32 42 44 60 62	-427078957998
SPT(16)	2062561687952367361	0 12 18 48 102 180 238 298 492 552 610 688 742 772 778 790	-53454392446
SPT(16)	2062561838807962909	0 4 22 54 70 82 112 120 124 132 162 174 190 222 240 244	97401203102
TPT(14)	2062562120331291641	0 2 18 20 60 62 96 98 168 170 210 212 228 230	378924531834
SPT(18)	2062562443967658029	0 24 42 50 60 102 108 122 174 218 270 284 290 332 342 350 368 392	702560898222
SPT(16)	2062563454384439579	0 48 72 180 192 198 258 278 294 314 374 380 392 500 524 572	1712977679772
SPT(16)	2062563641172178367	0 32 56 80 84 86 104 114 182 192 210 212 216 240 264 296	1899765418560