Prime p₀= 2788787181867607199 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 10 2 124 2 10 2 28 2 28 2 (?)
a_n: 0 2 30 32 42 44 168 170 180 182 210 212 240 242
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: 242
Found by: JonS
db: batch=82, k=14, 28 10 124 10 28 28

SPT(16)	2788785715261925117	0 14 56 60 62 102 162 170 186 194 254 294 296 300 342 356	-1466605682082
SPT(16)	2788786037841872161	0 10 16 36 52 88 108 112 186 190 210 246 262 282 288 298	-1144025735038
SPT(16)	2788786250131802731	0 12 28 42 48 52 90 108 142 160 198 202 208 222 238 250	-931735804468
SPT(16)	2788786361269316959	0 24 28 78 144 154 160 168 214 222 228 238 304 354 358 382	-820598290240
SPT(16)	2788786510765658419	0 52 64 90 112 210 294 300 304 310 394 492 514 540 552 604	-671101948780
SPT(18)	2788786900235201419	0 12 24 42 58 82 94 112 144 178 210 228 240 264 280 298 310 322	-281632405780
STPT(12)	2788787181867607199	0 2 30 32 42 44 168 170 180 182 210 212	0
SPT(16)	2788787443608104759	0 38 42 60 80 84 90 132 140 182 188 192 212 230 234 272	261740497560
SPT(16)	2788788282881678821	0 30 66 76 108 112 142 160 168 186 216 220 252 262 298 328	1101014071622
STPT(10)	2788788532242194327	0 2 24 26 42 44 60 62 84 86	1350374587128
STPT(10)	2788789053867482759	0 2 18 20 30 32 42 44 60 62	1871999875560