Prime p₀= 2112899007710476691 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 34 2 88 2 148 2 40 2 40 2 (?)
a_n: 0 2 60 62 96 98 186 188 336 338 378 380 420 422
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: 422
Found by: MarkRBright
db: batch=80, k=14, 58 34 88 148 40 40

SPT(16)	2112897089949518833	0 16 70 90 94 186 220 256 258 294 328 420 424 444 498 514	-1917760957858
SPT(16)	2112898043983708199	0 14 98 138 140 152 158 164 228 234 240 252 254 294 378 392	-963726768492
SPT(16)	2112898306014196303	0 4 36 58 70 94 100 124 210 234 240 264 276 298 330 334	-701696280388
SPT(16)	2112898468894818259	0 4 18 30 40 88 114 144 208 238 264 312 322 334 348 352	-538815658432
SPT(16)	2112898678614406153	0 58 64 78 120 130 144 148 210 214 228 238 280 294 300 358	-329096070538
TPT(14)	2112898967503310669	0 2 102 104 132 134 138 140 168 170 222 224 282 284	-40207166022
SPT(16)	2112899423546614277	0 24 54 72 84 86 92 102 134 144 150 152 164 182 212 236	415836137586
STPT(10)	2112899619723352247	0 2 12 14 72 74 132 134 144 146	612012875556
STPT(10)	2112899724843856841	0 2 6 8 48 50 90 92 96 98	717133380150
STPT(10)	2112899818129344149	0 2 42 44 90 92 138 140 180 182	810418867458
STPT(10)	2112900847556541737	0 2 30 32 60 62 90 92 120 122	1839846065046