Prime p₀= 826034441458894901 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 34 2 40 2 40 2 4 2 82 2 16 2 (?)
a_n: 0 2 36 38 78 80 120 122 126 128 210 212 228 230
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: 230
Found by: GLeeM
db: batch=73, k=14, 34 40 40 4 82 16

SPT(16)	826032969548942767	0 24 82 84 94 100 106 112 204 210 216 222 232 234 292 316	-1471909952134
SPT(16)	826032972240900271	0 22 42 70 72 78 82 130 180 228 232 238 240 268 288 310	-1469217994630
STPT(10)	826033426412167847	0 2 30 32 42 44 54 56 84 86	-1015046727054
STPT(10)	826033442232040697	0 2 30 32 72 74 114 116 144 146	-999226854204
SPT(16)	826033700312242043	0 14 24 56 66 74 86 90 164 168 180 188 198 230 240 254	-741146652858
SPT(16)	826033806013865773	0 4 10 60 150 168 184 216 298 330 346 364 454 504 510 514	-635445029128
STPT(10)	826034491179067109	0 2 42 44 60 62 78 80 120 122	49720172208
SPT(16)	826034582520518951	0 38 56 68 98 108 116 140 156 180 188 198 228 240 258 296	141061624050
STPT(10)	826034631152413391	0 2 36 38 78 80 120 122 156 158	189693518490
SPT(16)	826034636749495717	0 4 42 64 76 90 120 124 252 256 286 300 312 334 372 376	195290600816
STPT(10)	826034647542845561	0 2 6 8 18 20 30 32 36 38	206083950660