Prime p₀= 10574324044889321 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 4 2 70 2 16 2 40 2 106 2 40 2 (?)
a_n: 0 2 6 8 78 80 96 98 138 140 246 248 288 290
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: 290
Found by: Nosferatu*
db: batch=62, k=14, 4 70 16 40 106 40

SPT(14)	10574277830285321	0 18 20 36 42 48 62 96 110 116 122 138 140 158	-46214604000
TPT(12)	10574287319098421	0 2 48 50 78 80 90 92 198 200 270 272	-36725790900
TPT(12)	10574301625687727	0 2 30 32 42 44 72 74 114 116 132 134	-22419201594
SPT(14)	10574308181524921	0 12 52 58 100 162 190 228 256 318 360 366 406 418	-15863364400
SPT(14)	10574316720242123	0 24 44 60 66 80 98 216 234 248 254 270 290 314	-7324647198
SPT(14)	10574320044645913	0 30 36 40 64 78 96 178 196 210 234 238 244 274	-4000243408
SPT(14)	10574338127162101	0 10 42 48 52 78 102 238 262 288 292 298 330 340	14082272780
SPT(14)	10574338773054131	0 8 50 56 60 62 78 80 96 98 102 108 150 158	14728164810
SPT(14)	10574340765297247	0 4 30 42 60 70 120 136 186 196 214 226 252 256	16720407926
SPT(14)	10574342957466853	0 6 48 60 88 118 120 136 138 168 196 208 250 256	18912577532
SPT(14)	10574346745454377	0 6 22 34 54 64 90 106 132 142 162 174 190 196	22700565056