Prime p₀= 1245055693650910511 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 28 2 4 2 40 2 16 2 40 2 (?)
a_n: 0 2 30 32 60 62 66 68 108 110 126 128 168 170
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: 170
Found by: Megacruncher
db: batch=77, k=14, 28 28 4 40 16 40

TPT(14)	1245054599906725241	0 2 18 20 96 98 126 128 138 140 228 230 240 242	-1093744185270
STPT(10)	1245055007767779737	0 2 12 14 42 44 72 74 84 86	-685883130774
TPT(14)	1245055301032728329	0 2 102 104 132 134 138 140 180 182 258 260 390 392	-392618182182
STPT(10)	1245055418614387277	0 2 42 44 72 74 102 104 144 146	-275036523234
TPT(14)	1245055434955830437	0 2 84 86 90 92 102 104 120 122 162 164 240 242	-258695080074
STPT(10)	1245055436927721227	0 2 54 56 72 74 90 92 144 146	-256723189284
SPT(16)	1245055848442439717	0 14 26 32 50 54 90 110 126 146 182 186 204 210 222 236	154791529206
SPT(16)	1245055927398775313	0 8 26 66 90 104 110 138 176 204 210 224 248 288 306 314	233747864802
SPT(16)	1245055942230699139	0 30 48 90 118 120 162 172 228 238 280 282 310 352 370 400	248579788628
SPT(16)	1245056243350871671	0 52 66 70 118 132 168 196 222 250 286 300 348 352 366 418	549699961160
SPT(16)	1245056318652104891	0 18 32 38 72 78 86 108 140 162 170 176 210 216 230 248	625001194380