Prime p₀= 2121215721008806649 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 124 2 22 2 94 2 40 2 70 2 (?)
a_n: 0 2 12 14 138 140 162 164 258 260 300 302 372 374
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: 374
Found by: Landjunge
db: batch=80, k=14, 10 124 22 94 40 70

SPT(16)	2121214268716527641	0 26 42 60 72 98 126 152 216 242 270 296 308 326 342 368	-1452292279008
SPT(16)	2121215277273891131	0 42 56 68 72 78 86 90 98 102 110 116 120 132 146 188	-443734915518
TPT(14)	2121215358810805709	0 2 18 20 48 50 90 92 138 140 270 272 282 284	-362198000940
SPT(16)	2121215409065113133	0 14 36 48 54 66 104 134 180 210 248 260 266 278 300 314	-311943693516
SPT(16)	2121215423106047623	0 4 18 34 66 90 94 106 108 120 124 148 180 196 210 214	-297902759026
STPT(10)	2121215571022534277	0 2 12 14 132 134 252 254 264 266	-149986272372
TPT(14)	2121216203386831511	0 2 6 8 30 32 36 38 186 188 210 212 240 242	482378024862
STPT(10)	2121216490044088049	0 2 18 20 30 32 42 44 60 62	769035281400
SPT(16)	2121216691025462881	0 28 48 88 90 102 130 138 160 168 196 208 210 250 270 298	970016656232
SPT(16)	2121216855532299923	0 30 104 114 128 150 168 188 216 236 254 276 290 300 374 404	1134523493274
STPT(10)	2121216862547319539	0 2 30 32 60 62 90 92 120 122	1141538512890