Prime p₀= 2035581851807731781 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 34 2 10 2 58 2 16 2 88 2 (?)
a_n: 0 2 30 32 66 68 78 80 138 140 156 158 246 248
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: 248
Found by: Landjunge
db: batch=80, k=14, 28 34 10 58 16 88

SPT(16)	2035581234864456221	0 20 48 62 78 92 96 108 260 272 276 290 306 320 348 368	-616943275560
SPT(16)	2035581411937450879	0 54 64 90 94 120 124 168 244 288 292 318 322 348 358 412	-439870280902
SPT(16)	2035581619002805303	0 24 84 126 184 198 238 244 300 306 346 360 418 460 520 544	-232804926478
SPT(16)	2035581721104589711	0 40 60 100 130 190 226 240 256 270 306 366 396 436 456 496	-130703142070
SPT(16)	2035581727396722761	0 12 36 50 60 68 78 90 98 110 120 128 138 152 176 188	-124411009020
STPT(10)	2035581843625192361	0 2 36 38 78 80 120 122 156 158	-8182539420
SPT(16)	2035581929571166381	0 6 18 40 58 70 72 130 138 196 198 210 228 250 262 268	77763434600
SPT(16)	2035582577415288311	0 36 42 48 56 98 156 198 200 242 300 342 350 356 362 398	725607556530
STPT(10)	2035582807358185907	0 2 90 92 132 134 174 176 264 266	955550454126
SPT(16)	2035582971235179529	0 18 42 48 60 70 72 100 102 130 132 142 154 160 184 202	1119427447748
SPT(16)	2035583145739487933	0 8 24 30 68 78 108 128 246 266 296 306 344 350 366 374	1293931756152