Prime p₀= 927556587811126991 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 46 2 40 2 34 2 40 2 70 2 58 2 (?)
a_n: 0 2 48 50 90 92 126 128 168 170 240 242 300 302
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: 302
Found by: crashtech
db: batch=76, k=14, 46 40 34 40 70 58

STPT(10)	927556087306801781	0 2 6 8 48 50 90 92 96 98	-500504325210
STPT(10)	927556204777646201	0 2 6 8 18 20 30 32 36 38	-383033480790
STPT(10)	927556274161679507	0 2 42 44 72 74 102 104 144 146	-313649447484
SPT(16)	927556377898749317	0 12 60 80 110 132 144 180 236 272 284 306 336 356 404 416	-209912377674
SPT(18)	927556439195698261	0 36 48 60 88 108 126 136 178 270 312 322 340 360 388 400 412 448	-148615428730
TPT(14)	927556441242864227	0 2 90 92 174 176 222 224 252 254 300 302 312 314	-146568262764
SPT(16)	927556624046940241	0 12 40 58 78 90 112 118 120 126 148 160 180 198 226 238	36235813250
STPT(10)	927556844565345077	0 2 30 32 72 74 114 116 144 146	256754218086
SPT(16)	927556922130891517	0 12 40 72 84 100 112 124 222 234 246 262 274 306 334 346	334319764526
STPT(10)	927557015712910127	0 2 30 32 42 44 54 56 84 86	427901783136
STPT(10)	927557651822569679	0 2 18 20 30 32 42 44 60 62	1064011442688