Prime p₀= 2786136792554848121 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 4 2 22 2 124 2 22 2 16 2 10 2 (?)
a_n: 0 2 6 8 30 32 156 158 180 182 198 200 210 212
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: 212
Found by: JayPi
db: batch=82, k=14, 4 22 124 22 16 10

SPT(16)	2786136017676087281	0 8 18 60 86 98 162 168 200 206 270 282 308 350 360 368	-774878760840
STPT(10)	2786136031892513537	0 2 30 32 42 44 54 56 84 86	-760662334584
SPT(16)	2786136114105930181	0 10 16 36 46 52 70 88 120 138 156 162 172 192 198 208	-678448917940
SPT(16)	2786136229794297269	0 18 24 54 158 164 168 170 192 194 198 204 308 338 344 362	-562760550852
SPT(16)	2786136416620570219	0 30 34 42 90 94 178 222 280 324 408 412 460 468 472 502	-375934277902
STPT(10)	2786136772553613299	0 2 18 20 30 32 42 44 60 62	-20001234822
STPT(10)	2786136922814043047	0 2 12 14 72 74 132 134 144 146	130259194926
TPT(14)	2786137221924562769	0 2 18 20 30 32 72 74 222 224 258 260 282 284	429369714648
TPT(14)	2786137554159702737	0 2 150 152 210 212 222 224 252 254 294 296 324 326	761604854616
SPT(16)	2786137662660654073	0 4 28 70 76 88 90 114 160 184 186 198 204 246 270 274	870105805952
STPT(10)	2786137671364721957	0 2 90 92 132 134 174 176 264 266	878809873836