Prime p₀= 1121858507346226229 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 46 2 28 2 52 2 124 2 40 2 (?)
a_n: 0 2 60 62 108 110 138 140 192 194 318 320 360 362
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: 362
Found by: crashtech
db: batch=76, k=14, 58 46 28 52 124 40

SPT(16)	1121857432768148599	0 22 28 40 42 52 130 150 190 210 288 298 300 312 318 340	-1074578077630
SPT(13)	1121857502647771177	0 60 66 126 150 156 210 264 270 294 354 360 420	-1004698455052
STPT(10)	1121857564993733831	0 2 6 8 48 50 90 92 96 98	-942352492398
STPT(12)	1121857585063971359	0 2 30 32 42 44 48 50 60 62 90 92	-922282254870
STPT(10)	1121857816029980999	0 2 48 50 90 92 132 134 180 182	-691316245230
STPT(10)	1121858468219257577	0 2 30 32 42 44 54 56 84 86	-39126968652
STPT(10)	1121858536025732801	0 2 6 8 18 20 30 32 36 38	28679506572
STPT(10)	1121858684043988901	0 2 6 8 48 50 90 92 96 98	176697762672
SPT(16)	1121858827323774499	0 40 72 84 88 114 130 144 208 222 238 264 268 280 312 352	319977548270
STPT(10)	1121858851696555319	0 2 42 44 90 92 138 140 180 182	344350329090
SPT(16)	1121858959489108747	0 12 34 54 60 100 102 114 142 154 156 196 202 222 244 256	452142882518