Prime p₀= 2491573452563721971 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 16 2 76 2 58 2 10 2 40 2 28 2 (?)
a_n: 0 2 18 20 96 98 156 158 168 170 210 212 240 242
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: 242
Found by: Penguin
db: batch=82, k=14, 16 76 58 10 40 28

SPT(16)	2491572307904264759	0 18 38 144 150 158 168 192 230 254 264 272 278 384 404 422	-1144659457212
STPT(10)	2491572514425562619	0 2 18 20 30 32 42 44 60 62	-938138159352
SPT(16)	2491572569720908361	0 6 8 18 48 156 296 308 360 372 512 620 650 660 662 668	-882842813610
SPT(16)	2491572626034790229	0 2 8 18 38 60 72 78 122 128 140 162 182 192 198 200	-826528931742
TPT(14)	2491572807518247161	0 2 18 20 60 62 78 80 120 122 126 128 228 230	-645045474810
STPT(10)	2491573231455891431	0 2 30 32 60 62 90 92 120 122	-221107830540
SPT(16)	2491573608688334327	0 26 50 54 62 92 110 132 134 156 174 204 212 216 240 266	156124612356
SPT(16)	2491573789220390029	0 24 42 60 88 124 138 150 172 184 198 234 262 280 298 322	336656668058
STPT(10)	2491573908185647289	0 2 42 44 90 92 138 140 180 182	455621925318
SPT(16)	2491574077031085029	0 20 42 62 84 98 102 114 158 170 174 188 210 230 252 272	624467363058
STPT(10)	2491574140868642651	0 2 6 8 48 50 90 92 96 98	688304920680