Prime p₀= 58415490353625239 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 16 2 52 2 136 2 46 2 22 2 (?)
a_n: 0 2 30 32 48 50 102 104 240 242 288 290 312 314
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: 314
Found by: scrap
db: batch=67, k=14, 28 16 52 136 46 22

SPT(14)	58415420620737679	0 10 24 42 70 108 148 174 214 252 280 298 312 322	-69732887560
SPT(14)	58415420943930811	0 18 46 66 70 126 178 228 280 336 340 360 388 406	-69409694428
SPT(14)	58415446561712017	0 22 52 70 94 112 154 180 222 240 264 282 312 334	-43791913222
SPT(14)	58415452463947223	0 24 54 60 86 98 138 266 306 318 344 350 380 404	-37889678016
SPT(14)	58415452828552139	0 20 50 62 80 90 92 150 152 162 180 192 222 242	-37525073100
SPT(14)	58415458690773421	0 6 30 46 66 70 96 172 198 202 222 238 262 268	-31662851818
SPT(14)	58415531124804169	0 12 24 70 78 94 120 172 198 214 222 268 280 292	40771178930
SPT(14)	58415547194592857	0 20 36 44 66 84 86 90 92 110 132 140 156 176	56840967618
SPT(14)	58415590313774579	0 12 32 68 74 98 132 140 174 198 204 240 260 272	99960149340
TPT(12)	58415603600667449	0 2 42 44 78 80 90 92 138 140 162 164	113247042210
TPT(12)	58415605837031921	0 2 60 62 78 80 126 128 156 158 168 170	115483406682