Prime p₀= 800342502249554819 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 28 2 10 2 136 2 16 2 22 2 (?)
a_n: 0 2 60 62 90 92 102 104 240 242 258 260 282 284
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: amazing
db: batch=73, k=14, 58 28 10 136 16 22

SPT(16)	800341457688857473	0 34 48 76 120 138 166 180 184 198 226 244 288 316 330 364	-1044560697346
STPT(10)	800341567817392397	0 2 24 26 42 44 60 62 84 86	-934432162422
STPT(10)	800341670907886139	0 2 48 50 90 92 132 134 180 182	-831341668680
SPT(16)	800342039320674359	0 12 14 68 80 110 144 150 152 158 192 222 234 288 290 302	-462928880460
STPT(10)	800342074619030861	0 2 30 32 78 80 126 128 156 158	-427630523958
STPT(10)	800342092395230681	0 2 6 8 18 20 30 32 36 38	-409854324138
SPT(16)	800342535260717437	0 4 6 10 22 24 60 70 126 136 172 174 186 190 192 196	33011162618
STPT(10)	800343266018948591	0 2 30 32 60 62 90 92 120 122	763769393772
TPT(14)	800343295991411297	0 2 30 32 54 56 72 74 114 116 144 146 180 182	793741856478
SPT(16)	800343651763908209	0 42 48 68 138 158 182 188 192 198 222 242 312 332 338 380	1149514353390
SPT(16)	800343916035793919	0 12 14 44 62 84 128 152 210 234 278 300 318 348 350 362	1413786239100