Prime p₀= 2256729763218032981 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 154 2 52 2 34 2 28 2 82 2 (?)
a_n: 0 2 60 62 216 218 270 272 306 308 336 338 420 422
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: 422
Found by: Orange Kid
db: batch=81, k=14, 58 154 52 34 28 82

SPT(16)	2256728416741570589	0 12 24 38 44 48 60 104 108 152 164 168 174 188 200 212	-1346476462392
SPT(16)	2256728423393690219	0 18 50 68 78 84 98 114 164 180 194 200 210 228 260 278	-1339824342762
SPT(16)	2256728554282297111	0 48 76 78 106 148 150 168 220 238 240 282 310 312 340 388	-1208935735870
STPT(10)	2256728602207903259	0 2 18 20 60 62 102 104 120 122	-1161010129722
SPT(16)	2256728675701797953	0 50 60 68 78 104 116 138 266 288 300 326 336 344 354 404	-1087516235028
SPT(16)	2256729632135674769	0 42 54 72 90 108 110 150 152 192 194 212 230 248 260 302	-131082358212
SPT(13)	2256730006745712791	0 12 72 138 192 258 300 342 408 462 528 588 600	243527679810
STPT(12)	2256730056016690979	0 2 18 20 30 32 60 62 72 74 90 92	292798657998
SPT(16)	2256730186946767243	0 10 18 40 54 60 66 76 138 148 154 160 174 196 204 214	423728734262
STPT(10)	2256730515223015859	0 2 18 20 30 32 42 44 60 62	752004982878
SPT(16)	2256730837475828249	0 8 48 50 72 90 120 128 144 152 182 200 222 224 264 272	1074257795268