Prime p₀= 1408768688792820281 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 178 2 28 2 76 2 10 2 16 2 28 2 (?)
a_n: 0 2 180 182 210 212 288 290 300 302 318 320 348 350
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: phoenicis
db: batch=78, k=14, 178 28 76 10 16 28

SPT(16)	1408767540973560029	0 20 30 62 78 92 98 132 170 204 210 224 240 272 282 302	-1147819260252
STPT(10)	1408767729764086817	0 2 30 32 72 74 114 116 144 146	-959028733464
STPT(10)	1408767988712300141	0 2 30 32 78 80 126 128 156 158	-700080520140
SPT(16)	1408768095063341401	0 12 28 42 70 72 88 130 168 210 226 228 256 270 286 298	-593729478880
SPT(16)	1408768104149829827	0 32 42 54 62 110 182 222 314 354 426 474 482 494 504 536	-584642990454
STPT(10)	1408768164948094397	0 2 42 44 72 74 102 104 144 146	-523844725884
STPT(10)	1408768833860247029	0 2 18 20 30 32 42 44 60 62	145067426748
STPT(10)	1408768878774107969	0 2 18 20 30 32 42 44 60 62	189981287688
SPT(16)	1408769726425264501	0 28 42 48 82 100 130 132 166 168 198 216 250 256 270 298	1037632444220
SPT(16)	1408769875739407673	0 6 44 48 56 104 156 186 188 218 270 318 326 330 368 374	1186946587392
SPT(16)	1408769995336948691	0 20 62 90 102 108 116 152 186 222 230 236 248 276 318 338	1306544128410