Prime p₀= 2113002553817052431 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 46 2 28 2 40 2 34 2 58 2 22 2 (?)
a_n: 0 2 48 50 78 80 120 122 156 158 216 218 240 242
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: Landjunge
db: batch=80, k=14, 46 28 40 34 58 22

SPT(16)	2112999843682324901	0 50 80 120 126 146 176 252 386 462 492 512 518 558 588 638	-2710134727530
SPT(16)	2112999981687138281	0 2 26 36 38 66 108 110 138 140 182 210 212 222 246 248	-2572129914150
SPT(16)	2113000676677245851	0 68 132 138 188 192 228 242 306 320 356 360 410 416 480 548	-1877139806580
STPT(10)	2113001604092589737	0 2 90 92 102 104 114 116 204 206	-949724462694
TPT(14)	2113001669781570569	0 2 42 44 72 74 150 152 180 182 240 242 408 410	-884035481862
STPT(10)	2113001953766620517	0 2 42 44 72 74 102 104 144 146	-600050431914
SPT(16)	2113002702542915839	0 12 40 42 64 84 102 130 144 172 190 210 232 234 262 274	148725863408
SPT(16)	2113003030449075679	0 12 22 48 132 148 162 168 214 220 234 250 334 360 370 382	476632023248
SPT(16)	2113003377792452377	0 12 36 60 66 112 136 144 172 180 204 250 256 280 304 316	823975399946
SPT(16)	2113003601806217371	0 18 28 30 52 58 66 72 166 172 180 186 208 210 220 238	1047989164940
SPT(16)	2113003937683684657	0 24 96 100 112 132 154 166 360 372 394 414 426 430 502 526	1383866632226