Prime p₀= 1117628619555038027 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 82 2 64 2 70 2 70 2 94 2 22 2 (?)
a_n: 0 2 84 86 150 152 222 224 294 296 390 392 414 416
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: 416
Found by: crashtech
db: batch=76, k=14, 82 64 70 70 94 22

SPT(16)	1117628136159678167	0 30 96 110 150 192 230 272 300 342 380 422 462 476 542 572	-483395359860
STPT(10)	1117628141071447301	0 2 6 8 18 20 30 32 36 38	-478483590726
SPT(16)	1117628167654294979	0 18 42 68 102 134 210 222 260 272 348 380 414 440 464 482	-451900743048
SPT(16)	1117628190867584743	0 34 36 90 118 130 138 144 190 196 204 216 244 298 300 334	-428687453284
STPT(10)	1117628227865332217	0 2 60 62 72 74 84 86 144 146	-391689705810
SPT(16)	1117628612952350797	0 36 42 46 60 82 114 124 162 172 204 226 240 244 250 286	-6602687230
STPT(10)	1117628772046827581	0 2 30 32 78 80 126 128 156 158	152491789554
TPT(14)	1117629227480052281	0 2 120 122 126 128 156 158 198 200 210 212 276 278	607925014254
TPT(14)	1117629326492288549	0 2 30 32 162 164 168 170 240 242 288 290 342 344	706937250522
STPT(10)	1117629597206023799	0 2 18 20 30 32 42 44 60 62	977650985772
STPT(12)	1117629619173370739	0 2 18 20 42 44 78 80 102 104 120 122	999618332712