Prime p₀= 862706422211314097 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 16 2 10 2 100 2 46 2 88 2 (?)
a_n: 0 2 42 44 60 62 72 74 174 176 222 224 312 314
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: 314
Found by: scrap
db: batch=73, k=14, 40 16 10 100 46 88

SPT(16)	862705743702877817	0 12 36 56 92 144 152 182 204 234 242 294 330 350 374 386	-678508436280
SPT(16)	862705915237892917	0 6 10 24 72 120 154 156 190 192 226 274 322 336 340 346	-506973421180
SPT(16)	862705963222105973	0 26 36 54 98 126 236 276 278 318 428 456 500 518 528 554	-458989208124
STPT(10)	862705980627155099	0 2 78 80 120 122 162 164 240 242	-441584158998
STPT(10)	862706079734675357	0 2 30 32 42 44 54 56 84 86	-342476638740
STPT(10)	862706177177141327	0 2 30 32 60 62 90 92 120 122	-245034172770
SPT(16)	862706509992767897	0 2 14 30 36 56 86 120 176 210 240 260 266 282 294 296	87781453800
TPT(14)	862706928222208919	0 2 42 44 90 92 120 122 132 134 150 152 210 212	506010894822
SPT(16)	862707020770555319	0 24 30 42 72 80 84 104 108 128 132 140 170 182 188 212	598559241222
SPT(16)	862707184093146341	0 6 20 32 56 120 126 152 210 236 242 306 330 342 356 362	761881832244
TPT(14)	862707455689887341	0 2 30 32 48 50 78 80 120 122 186 188 198 200	1033478573244