Prime p₀= 2136079588074890039 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 76 2 58 2 70 2 106 2 52 2 (?)
a_n: 0 2 30 32 108 110 168 170 240 242 348 350 402 404
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: 404
Found by: [SG-2W]Kurzer
db: batch=80, k=14, 28 76 58 70 106 52

SPT(16)	2136078859625214689	0 12 44 188 210 258 264 278 294 308 314 362 384 528 560 572	-728449675350
STPT(10)	2136079254012376571	0 2 66 68 108 110 150 152 216 218	-334062513468
SPT(16)	2136079282604172793	0 24 46 90 94 118 138 150 154 166 186 210 214 258 280 304	-305470717246
SPT(16)	2136079354608013447	0 42 96 106 154 166 180 196 210 226 240 252 300 310 364 406	-233466876592
STPT(10)	2136079406349682877	0 2 30 32 72 74 114 116 144 146	-181725207162
STPT(10)	2136079464633996197	0 2 30 32 42 44 54 56 84 86	-123440893842
SPT(16)	2136080009972733271	0 10 12 28 46 52 76 82 96 102 126 132 150 166 168 178	421897843232
STPT(10)	2136080092937793227	0 2 30 32 42 44 54 56 84 86	504862903188
STPT(12)	2136080177777504111	0 2 30 32 60 62 96 98 126 128 156 158	589702614072
STPT(10)	2136080322300412751	0 2 6 8 48 50 90 92 96 98	734225522712
TPT(14)	2136080356016840897	0 2 30 32 180 182 222 224 234 236 240 242 360 362	767941950858