Prime p₀= 2341241290544954267 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 88 2 70 2 28 2 40 2 28 2 (?)
a_n: 0 2 30 32 120 122 192 194 222 224 264 266 294 296
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: 296
Found by: eclipse99
db: batch=81, k=14, 28 88 70 28 40 28

SPT(16)	2341240147411777583	0 74 104 108 144 156 168 228 236 296 308 320 356 360 390 464	-1143133176684
STPT(10)	2341240163808213287	0 2 42 44 72 74 102 104 144 146	-1126736740980
STPT(10)	2341240311303954029	0 2 12 14 30 32 48 50 60 62	-979241000238
SPT(16)	2341240734422722157	0 6 20 32 50 90 174 176 180 182 266 306 324 336 350 356	-556122232110
SPT(16)	2341241023262238197	0 6 14 24 44 74 84 90 116 122 132 162 182 192 200 206	-267282716070
STPT(10)	2341241181254451767	0 2 54 56 132 134 210 212 264 266	-109290502500
SPT(16)	2341241334157011343	0 10 18 36 78 114 136 148 186 198 220 256 298 316 324 334	43612057076
SPT(16)	2341241441064187157	0 12 20 30 42 80 86 90 122 126 132 170 182 192 200 212	150519232890
SPT(16)	2341241454985909499	0 24 48 50 60 122 128 162 170 204 210 272 282 284 308 332	164440955232
TPT(14)	2341241885896066499	0 2 78 80 90 92 108 110 150 152 162 164 192 194	595351112232
SPT(16)	2341242146860751377	0 12 40 42 70 112 124 172 174 222 234 276 304 306 334 346	856315797110