Prime p₀= 2950459047345218819 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 16 2 112 2 64 2 250 2 220 2 4 2 (?)
a_n: 0 2 18 20 132 134 198 200 450 452 672 674 678 680
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: 680
Found by: Landjunge
db: batch=82, k=14, 16 112 64 250 220 4

SPT(16)	2950457182833933499	0 4 12 34 48 58 70 84 88 102 114 124 138 160 168 172	-1864511285320
STPT(10)	2950457563790681897	0 2 30 32 120 122 210 212 240 242	-1483554536922
SPT(13)	2950458156182681623	0 30 48 84 114 150 174 198 234 264 300 318 348	-891162537196
SPT(16)	2950458291104534797	0 34 70 82 90 112 124 160 186 222 234 256 264 276 312 346	-756240684022
SPT(16)	2950458801431772901	0 6 30 70 106 112 132 142 180 190 210 216 252 292 316 322	-245913445918
STPT(10)	2950458907679526977	0 2 30 32 42 44 54 56 84 86	-139665691842
SPT(16)	2950459205908471291	0 12 42 90 132 156 168 222 256 310 322 346 388 436 466 478	158563252472
STPT(10)	2950459405707634937	0 2 30 32 42 44 54 56 84 86	358362416118
SPT(16)	2950459499380552729	0 42 48 70 72 84 114 120 202 208 238 250 252 274 280 322	452035333910
SPT(16)	2950459524688934449	0 22 24 60 78 102 112 148 174 210 220 244 262 298 300 322	477343715630
STPT(10)	2950459597032228551	0 2 6 8 48 50 90 92 96 98	549687009732