Prime p₀= 2736888278362247957 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 22 2 28 2 64 2 58 2 28 2 22 2 (?)
a_n: 0 2 24 26 54 56 120 122 180 182 210 212 234 236
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: 236
Found by: arkiss
db: batch=82, k=14, 22 28 64 58 28 22

SPT(16)	2736887126039121961	0 36 42 48 70 72 76 90 178 192 196 198 220 226 232 268	-1152323125996
SPT(16)	2736887419760052563	0 6 8 26 50 86 210 236 240 266 390 426 450 468 470 476	-858602195394
SPT(16)	2736887664502310551	0 16 18 66 82 88 102 108 130 136 150 156 172 220 222 238	-613859937406
STPT(10)	2736887985913377377	0 2 54 56 72 74 90 92 144 146	-292448870580
STPT(10)	2736888126481218761	0 2 6 8 18 20 30 32 36 38	-151881029196
TPT(14)	2736888202570293389	0 2 48 50 78 80 120 122 210 212 288 290 300 302	-75791954568
STPT(10)	2736888551218001429	0 2 18 20 30 32 42 44 60 62	272855753472
SPT(16)	2736888605151692077	0 42 120 144 184 186 256 262 294 300 370 372 412 436 514 556	326789444120
STPT(10)	2736888699756682787	0 2 30 32 42 44 54 56 84 86	421394434830
SPT(16)	2736889257491641423	0 10 54 66 78 84 100 106 168 174 190 196 208 220 264 274	979129393466
STPT(10)	2736889292670419009	0 2 12 14 30 32 48 50 60 62	1014308171052