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2020-07-05, 16:11   #860
sweety439

Nov 2016

13·173 Posts

We don't know the conjectures yet on bases 66, 120, 156, 180, 210, 240, 280, 330, 358, 420, 456, 462, 546, ... and Sierp 190, 540 and Riesel 276, 486. They are definitely k > 1M. They're just too unmanageable with today's computing power and knowledge. That said, if people are open to the idea, I might suggest searching some of those up to k=100K at some point to get future generations of prime searchers started on those huge efforts. To me, the main thing is collecting data for us and for future generations to analyze.

There are upper bounds of these conjectures: (the lower bounds of these conjectures are all 1000001, since all k<=1M are checked)

S66: 21314443 (if not this number, then must be == 4 mod 5 or == 12 mod 13)
S120: 374876369 (if not this number, then must be == 6 mod 7 or == 16 mod 17)
S156: 18406311208 (if not this number, then must be == 4 mod 5 or == 30 mod 31)
S180: 1679679 (if not this number, then must be == 178 mod 179)
S190: 3146151 (if not this number, then must be == 2 mod 3 or == 6 mod 7)
S210: 147840103 (if not this number, then must be == 10 mod 11 or == 18 mod 19)
S240: 1722187 (if not this number, then must be == 238 mod 239)
S280: 82035074042274 (if not this number, then must be == 2 mod 3 or == 30 mod 31)
S330: 16636723 (if not this number, then must be == 6 mod 7 or == 46 mod 47)
S358: 27478218 (if not this number, then must be == 2 mod 3 or == 6 mod 7 or == 16 mod 17)
S420: 2288555 (if not this number, then must be == 418 mod 419)
S456: 14836963 (if not this number, then must be == 4 mod 5 or == 6 mod 7 or == 12 mod 13)
S462: 6880642 (if not this number, then must be == 460 mod 461)
S540: 1091739 (if not this number, then must be == 6 mod 7 or == 10 mod 11)
S546: 45119296 (if not this number, then must be == 4 mod 5 or == 108 mod 109)

R66: 101954772 (if not this number, then must be == 1 mod 5 or == 1 mod 13)
R120: 166616308 (if not this number, then must be == 1 mod 7 or == 1 mod 17)
R156: 2113322677 (if not this number, then must be == 1 mod 5 or == 1 mod 31)
R180: 7674582 (if not this number, then must be == 1 mod 179)
R210: 80176412 (if not this number, then must be == 1 mod 11 or == 1 mod 19)
R240: 2952972 (if not this number, then must be == 1 mod 239)
R276: 1552307 (if not this number, then must be == 1 mod 5 or == 1 mod 11)
R280: 513613045571841 (if not this number, then must be == 1 mod 3 or == 1 mod 31)
R330: 16527822 (if not this number, then must be == 1 mod 7 or == 1 mod 47)
R358: 27606383 (if not this number, then must be == 1 mod 3 or == 1 mod 7 or == 1 mod 17)
R420: 6548233 (if not this number, then must be == 1 mod 419)
R456: 76303920 (if not this number, then must be == 1 mod 5 or == 1 mod 7 or == 1 mod 13)
R462: 2924772 (if not this number, then must be == 1 mod 461)
R486: 1525283 (if not this number, then must be == 1 mod 5 or == 1 mod 97)
Attached Files
 Conjectured smallest Sierpinski number.txt (8.3 KB, 3 views) Conjectured smallest Riesel number.txt (8.3 KB, 1 views)

Last fiddled with by sweety439 on 2020-07-10 at 16:26