Prime p₀= 1021236002921087909 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 16 2 28 2 118 2 10 2 40 2 124 2 (?)
a_n: 0 2 18 20 48 50 168 170 180 182 222 224 348 350
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: 350
Found by: Spectrum
db: batch=76, k=14, 16 28 118 10 40 124

STPT(10)	1021235290557370307	0 2 12 14 42 44 72 74 84 86	-712363717602
STPT(10)	1021235335374648179	0 2 30 32 60 62 90 92 120 122	-667546439730
TPT(14)	1021235724319389911	0 2 36 38 48 50 78 80 168 170 180 182 288 290	-278601697998
TPT(14)	1021235800412600987	0 2 12 14 60 62 84 86 222 224 240 242 342 344	-202508486922
STPT(10)	1021235810385179531	0 2 6 8 18 20 30 32 36 38	-192535908378
STPT(10)	1021235883797979797	0 2 54 56 132 134 210 212 264 266	-119123108112
SPT(16)	1021236027820711061	0 6 20 32 50 78 86 108 140 162 170 198 216 228 242 248	24899623152
SPT(16)	1021236189130680737	0 2 54 86 102 104 140 146 180 186 222 224 240 272 324 326	186209592828
SPT(16)	1021236223083215809	0 4 60 64 70 90 108 118 120 130 148 168 174 178 234 238	220162127900
STPT(10)	1021236290374251617	0 2 30 32 42 44 54 56 84 86	287453163708
SPT(16)	1021236504698450023	0 34 36 54 88 90 124 144 190 210 244 246 280 298 300 334	501777362114