Prime p₀= 976359008762579639 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 76 2 28 2 22 2 34 2 172 2 (?)
a_n: 0 2 30 32 108 110 138 140 162 164 198 200 372 374
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: 374
Found by: Theadalus
db: batch=76, k=14, 28 76 28 22 34 172

SPT(20)	976357926080239081	0 10 16 22 36 46 66 78 88 96 112 120 130 142 162 172 186 192 198 208	-1082682340558
SPT(16)	976358159876242277	0 2 50 54 66 102 134 222 224 312 344 380 392 396 444 446	-848886337362
SPT(16)	976358498971513519	0 4 10 72 82 130 138 154 168 184 192 240 250 312 318 322	-509791066120
SPT(16)	976358548705715033	0 26 36 78 80 126 158 188 348 378 410 456 458 500 510 536	-460056864606
SPT(16)	976358784565163227	0 4 22 40 54 76 82 100 186 204 210 232 246 264 282 286	-224197416412
SPT(16)	976358796791086967	0 14 20 44 62 84 104 122 174 192 212 234 252 276 282 296	-211971492672
STPT(10)	976359273300858677	0 2 24 26 42 44 60 62 84 86	264538279038
SPT(16)	976359344490773311	0 18 22 52 60 66 136 148 150 162 232 238 246 276 280 298	335728193672
SPT(16)	976359367378433473	0 10 40 64 70 94 96 120 130 154 156 180 186 210 240 250	358615853834
SPT(16)	976359522010845541	0 28 60 88 100 106 126 160 186 220 240 246 258 286 318 346	513248265902
STPT(10)	976359619646449079	0 2 18 20 30 32 42 44 60 62	610883869440