Prime p₀= 1266452874143098427 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 10 2 58 2 16 2 40 2 76 2 (?)
a_n: 0 2 30 32 42 44 102 104 120 122 162 164 240 242
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: Megacruncher
db: batch=77, k=14, 28 10 58 16 40 76

SPT(16)	1266451579867698401	0 2 6 8 60 78 90 92 156 158 170 188 240 242 246 248	-1294275400026
SPT(16)	1266451750043534479	0 10 24 34 120 168 178 208 330 360 370 418 504 514 528 538	-1124099563948
SPT(16)	1266452041337365969	0 10 60 100 130 144 154 198 214 258 268 282 312 352 402 412	-832805732458
SPT(16)	1266452207262151963	0 16 36 40 54 58 70 76 78 84 96 100 114 118 138 154	-666880946464
STPT(10)	1266452608107016019	0 2 18 20 30 32 42 44 60 62	-266036082408
STPT(10)	1266452854504899179	0 2 18 20 30 32 42 44 60 62	-19638199248
SPT(16)	1266452903626540951	0 12 18 52 100 102 118 132 178 192 208 210 258 292 298 310	29483442524
TPT(14)	1266453036444049787	0 2 60 62 102 104 144 146 240 242 300 302 420 422	162300951360
TPT(14)	1266453055521548747	0 2 12 14 24 26 30 32 84 86 144 146 210 212	181378450320
STPT(10)	1266453585840910937	0 2 30 32 42 44 54 56 84 86	711697812510
SPT(16)	1266453864909724181	0 8 48 56 62 78 140 146 162 168 230 246 252 260 300 308	990766625754