Prime p₀= 2111998055908522709 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 46 2 22 2 28 2 64 2 82 2 58 2 (?)
a_n: 0 2 48 50 72 74 102 104 168 170 252 254 312 314
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: 314
Found by: gemini8
db: batch=80, k=14, 46 22 28 64 82 58

SPT(16)	2111996719327524163	0 28 36 54 58 70 94 106 198 210 234 246 250 268 276 304	-1336580998546
SPT(16)	2111997068786359621	0 12 42 48 66 72 96 126 142 172 196 202 220 226 256 268	-987122163088
SPT(16)	2111997482994320197	0 40 64 66 112 124 126 132 154 160 162 174 220 222 246 286	-572914202512
SPT(16)	2111997525190451357	0 2 42 72 86 104 110 132 134 156 162 180 194 224 264 266	-530718071352
STPT(10)	2111997882555944837	0 2 24 26 42 44 60 62 84 86	-173352577872
SPT(16)	2111997895754363417	0 62 72 86 140 152 176 236 240 300 324 336 390 404 414 476	-160154159292
SPT(16)	2111998058366483437	0 34 82 96 124 126 142 160 216 234 250 252 280 294 342 376	2457960728
SPT(16)	2111998314845997551	0 18 32 42 68 80 96 110 198 212 228 240 266 276 290 308	258937474842
STPT(10)	2111998327997908289	0 2 18 20 60 62 102 104 120 122	272089385580
STPT(10)	2111998356080666237	0 2 30 32 60 62 90 92 120 122	300172143528
STPT(10)	2111998433041582367	0 2 60 62 72 74 84 86 144 146	377133059658