Prime p₀= 789046825696067429 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 76 2 58 2 22 2 4 2 70 2 10 2 (?)
a_n: 0 2 78 80 138 140 162 164 168 170 240 242 252 254
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: 254
Found by: [SG]FX
db: batch=73, k=14, 76 58 22 4 70 10

SPT(16)	789046271642994913	0 18 48 84 118 126 130 148 216 234 238 246 280 316 346 364	-554053072516
SPT(16)	789046351406060203	0 24 36 40 60 66 78 84 190 196 208 214 234 238 250 274	-474290007226
SPT(16)	789046614457492997	0 6 14 20 30 60 72 84 92 104 116 146 156 162 170 176	-211238574432
SPT(16)	789046644939864029	0 14 42 50 60 78 98 110 132 144 164 182 192 200 228 242	-180756203400
STPT(10)	789046657093985177	0 2 30 32 42 44 54 56 84 86	-168602082252
STPT(10)	789046664690156567	0 2 60 62 102 104 144 146 204 206	-161005910862
SPT(16)	789046833648567233	0 24 50 84 104 134 138 150 164 176 180 210 230 264 290 314	7952499804
STPT(10)	789047150761285847	0 2 30 32 72 74 114 116 144 146	325065218418
SPT(16)	789047176134309707	0 26 66 84 140 150 174 236 270 332 356 366 422 440 480 506	350438242278
TPT(14)	789047391844506101	0 2 30 32 126 128 156 158 168 170 180 182 270 272	566148438672
STPT(12)	789047473988494949	0 2 18 20 42 44 48 50 72 74 90 92	648292427520