Prime p₀= 816459708512554541 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 34 2 52 2 16 2 58 2 88 2 (?)
a_n: 0 2 30 32 66 68 120 122 138 140 198 200 288 290
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: 290
Found by: [SG]FX
db: batch=73, k=14, 28 34 52 16 58 88

SPT(16)	816458923269010699	0 10 12 30 34 42 54 60 82 88 100 108 112 130 132 142	-785243543842
SPT(18)	816459074088440287	0 16 40 70 72 94 112 150 180 196 226 264 282 304 306 336 360 376	-634424114254
STPT(10)	816459208819852649	0 2 18 20 30 32 42 44 60 62	-499692701892
SPT(16)	816459379460929969	0 52 72 112 120 150 174 198 274 298 322 352 360 400 420 472	-329051624572
TPT(14)	816459403141553291	0 2 96 98 198 200 240 242 246 248 306 308 360 362	-305371001250
SPT(16)	816459462814526593	0 6 10 28 84 88 90 108 286 304 306 310 366 384 388 394	-245698027948
STPT(10)	816460223468379899	0 2 12 14 90 92 168 170 180 182	514955825358
STPT(10)	816460347658557269	0 2 48 50 90 92 132 134 180 182	639146002728
STPT(10)	816460638017289821	0 2 6 8 48 50 90 92 96 98	929504735280
STPT(10)	816460849431193739	0 2 12 14 90 92 168 170 180 182	1140918639198
STPT(10)	816460923114395057	0 2 42 44 72 74 102 104 144 146	1214601840516