Prime p₀= 2157874475697016031 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 16 2 40 2 28 2 4 2 40 2 16 2 (?)
a_n: 0 2 18 20 60 62 90 92 96 98 138 140 156 158
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: 158
Found by: Landjunge
db: batch=81, k=14, 16 40 28 4 40 16

SPT(16)	2157873028550299063	0 16 40 64 66 78 106 150 154 198 226 238 240 264 288 304	-1447146716968
STPT(10)	2157873029511968147	0 2 30 32 42 44 54 56 84 86	-1446185047884
TPT(14)	2157873080340977849	0 2 48 50 78 80 90 92 132 134 150 152 192 194	-1395356038182
STPT(10)	2157873089668254977	0 2 42 44 72 74 102 104 144 146	-1386028761054
SPT(16)	2157873225161832449	0 14 38 42 60 98 102 104 138 140 144 182 200 204 228 242	-1250535183582
SPT(16)	2157874271237283623	0 14 48 68 138 140 146 168 176 198 204 206 276 296 330 344	-204459732408
TPT(14)	2157875034324636701	0 2 6 8 48 50 60 62 138 140 216 218 240 242	558627620670
TPT(14)	2157875323312724357	0 2 84 86 114 116 144 146 192 194 312 314 570 572	847615708326
SPT(16)	2157875414073160349	0 14 44 60 72 98 102 120 122 140 144 170 182 198 228 242	938376144318
SPT(16)	2157875963566270609	0 4 12 154 162 238 252 270 292 310 324 400 408 550 558 562	1487869254578
SPT(16)	2157876012998877961	0 6 40 58 60 88 102 132 136 166 180 208 210 228 262 268	1537301861930