Prime p₀= 261190535162340569 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 10 2 16 2 40 2 16 2 10 2 (?)
a_n: 0 2 30 32 42 44 60 62 102 104 120 122 132 134
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: desktop64
db: batch=69, k=14, 28 10 16 40 16 10

SPT(14)	261190424486200939	0 48 52 72 78 88 100 162 174 184 190 210 214 262	-110676139630
SPT(14)	261190441226711999	0 62 74 80 150 162 182 192 212 224 294 300 312 374	-93935628570
SPT(14)	261190457833766023	0 10 28 34 54 90 120 124 154 190 210 216 234 244	-77328574546
SPT(14)	261190459754745239	0 20 32 120 140 188 200 210 222 270 290 378 390 410	-75407595330
SPT(16)	261190479694693343	0 6 54 56 60 104 144 146 174 176 216 260 264 266 314 320	-55467647226
TPT(12)	261190521169205597	0 2 54 56 102 104 114 116 180 182 210 212	-13993134972
STPT(12)	261190535162340599	0 2 12 14 30 32 72 74 90 92 102 104	30
TPT(12)	261190546683328109	0 2 150 152 210 212 222 224 240 242 282 284	11520987540
SPT(14)	261190550090823767	0 14 36 56 86 126 156 254 284 324 354 374 396 410	14928483198
SPT(16)	261190561720488889	0 24 42 58 118 130 144 168 244 268 282 294 354 370 388 412	26558148320
SPT(14)	261190576059642577	0 60 64 82 96 124 150 166 192 220 234 252 256 316	40897302008