Prime p₀= 2816867878722986069 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 16 2 22 2 4 2 10 2 40 2 28 2 (?)
a_n: 0 2 18 20 42 44 48 50 60 62 102 104 132 134
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: 134
Found by: [SG-FC] hl
db: batch=82, k=14, 16 22 4 10 40 28

SPT(16)	2816867250439155733	0 10 30 54 58 88 94 114 124 144 150 180 184 208 228 238	-628283830336
SPT(16)	2816867278001214673	0 48 70 114 138 148 174 184 264 274 300 310 334 378 400 448	-600721771396
SPT(16)	2816867357186302229	0 8 14 20 62 98 122 132 140 150 174 210 252 258 264 272	-521536683840
SPT(16)	2816867763129479179	0 40 42 52 108 112 120 142 150 172 180 184 240 250 252 292	-115593506890
STPT(10)	2816867784470016029	0 2 18 20 30 32 42 44 60 62	-94252970040
SPT(16)	2816867851631596627	0 16 34 100 106 142 144 156 160 172 174 210 216 282 300 316	-27091389442
SPT(16)	2816868125147805437	0 20 24 126 176 186 200 216 260 276 290 300 350 452 456 476	246424819368
SPT(16)	2816868766902933913	0 4 10 36 46 88 118 130 174 186 216 258 268 294 300 304	888179947844
STPT(10)	2816868897573384527	0 2 30 32 42 44 54 56 84 86	1018850398458
STPT(10)	2816868918998230667	0 2 84 86 132 134 180 182 264 266	1040275244598
SPT(16)	2816869324313769031	0 16 88 126 150 168 172 220 258 306 310 328 352 390 462 478	1445590782962