Prime p₀= 2068676990263753811 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 106 2 28 2 28 2 58 2 106 2 (?)
a_n: 0 2 30 32 138 140 168 170 198 200 258 260 366 368
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: 368
Found by: Cruncher Pete
db: batch=80, k=14, 28 106 28 28 58 106

SPT(16)	2068675746158775409	0 12 18 28 120 130 160 190 192 222 252 262 354 364 370 382	-1244104978402
STPT(10)	2068676001558623591	0 2 36 38 78 80 120 122 156 158	-988705130220
SPT(16)	2068676081775255157	0 6 46 72 100 106 112 154 162 204 210 216 244 270 310 316	-908488498654
SPT(16)	2068676370104049799	0 10 18 22 52 114 118 130 132 144 148 210 240 244 252 262	-620159704012
STPT(10)	2068676762822452199	0 2 18 20 30 32 42 44 60 62	-227441301612
TPT(14)	2068676936968004327	0 2 24 26 54 56 72 74 84 86 150 152 252 254	-53295749484
SPT(16)	2068678997514111737	0 72 102 156 170 192 234 236 240 242 284 306 320 374 404 476	2007250357926
TPT(14)	2068679546610119501	0 2 36 38 78 80 90 92 126 128 168 170 186 188	2556346365690
SPT(16)	2068679816196668399	0 2 8 20 44 60 102 104 168 170 212 228 252 264 270 272	2825932914588
STPT(10)	2068680054084361967	0 2 30 32 42 44 54 56 84 86	3063820608156
SPT(16)	2068680191445808933	0 10 48 58 76 100 124 156 178 210 234 258 276 286 324 334	3201182055122