Prime p₀= 2097860240014221281 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 64 2 70 2 28 2 28 2 40 2 (?)
a_n: 0 2 60 62 126 128 198 200 228 230 258 260 300 302
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: matsu_pl
db: batch=80, k=14, 58 64 70 28 28 40

SPT(16)	2097858476089814327	0 32 42 80 96 162 182 222 224 264 284 350 366 404 414 446	-1763924406954
TPT(14)	2097858524598859667	0 2 12 14 72 74 84 86 192 194 210 212 240 242	-1715415361614
SPT(16)	2097858590620002751	0 16 36 46 52 72 76 88 90 102 106 126 132 142 162 178	-1649394218530
STPT(10)	2097858648611556539	0 2 42 44 60 62 78 80 120 122	-1591402664742
STPT(10)	2097859405480886777	0 2 30 32 72 74 114 116 144 146	-834533334504
SPT(16)	2097859565016336113	0 6 48 66 90 128 144 146 168 170 186 224 248 266 308 314	-674997885168
STPT(10)	2097860364297306977	0 2 30 32 42 44 54 56 84 86	124283085696
STPT(10)	2097860881258613927	0 2 30 32 42 44 54 56 84 86	641244392646
STPT(10)	2097861239811700331	0 2 78 80 168 170 258 260 336 338	999797479050
SPT(13)	2097861258824900137	0 24 60 72 114 144 192 240 270 312 324 360 384	1018810678856
SPT(16)	2097862052734460063	0 20 56 60 78 104 108 174 200 266 270 296 314 318 354 374	1812720238782