A: “The number of prime factors of 4678946132165798721321 is divisible by 3”
B: “The number of prime factors of 9876216987326578968732678968432126877 8498415465468 5432159878453213659873 1987654164163415874987 3674145748126589681321826878 79216876516857651 64549687962165468765632 132185913574684613213557 is divisible by 2”
P(F(A)) is about 1⁄3 and P(F(B)) is about 1⁄2.
But it’s far more likely that someone will bother to prove A, just because the number is much smaller.
ETA: To clarify, I don’t expect it to be particularly hard to prove or disprove, I just don’t think anyone will bother.
Whether someone will bother really depends on why someone wants to know. You can simple type “primefactors of 9876216987326578968732678968432126877” into Wolfram Alpha and get your answer. It’s not harder than typing “primefactors of 4678946132165798721321″ into Wolfram Alpha
I don’t know if this was due to an edit, but the second number in Khoth’s post is far larger than 9876216987326578968732678968432126877, and indeed Alpha won’t factor it.
To be honest I’m sort of surprised that Alpha is happy to factor 4678946132165798721321, I’d have thought that that was already too large.
The reason nobody will bother is that it’s just one 200 digit number among another 10^200 similar numbers. Even if you care about one of them enough to ask Wolfram Alpha, it’s vanishingly unlikely to be that particular one.
Technically it is harder, since there are more digits; apart from the additional work involved this also makes more opportunities for mistakes. In addition, of course, the computer at the other end is going to have to do more work.
How about the statements:
A: “The number of prime factors of 4678946132165798721321 is divisible by 3”
B: “The number of prime factors of 9876216987326578968732678968432126877 8498415465468 5432159878453213659873 1987654164163415874987 3674145748126589681321826878 79216876516857651 64549687962165468765632 132185913574684613213557 is divisible by 2”
P(F(A)) is about 1⁄3 and P(F(B)) is about 1⁄2.
But it’s far more likely that someone will bother to prove A, just because the number is much smaller.
ETA: To clarify, I don’t expect it to be particularly hard to prove or disprove, I just don’t think anyone will bother.
Whether someone will bother really depends on why someone wants to know. You can simple type “primefactors of 9876216987326578968732678968432126877” into Wolfram Alpha and get your answer. It’s not harder than typing “primefactors of 4678946132165798721321″ into Wolfram Alpha
I don’t know if this was due to an edit, but the second number in Khoth’s post is far larger than 9876216987326578968732678968432126877, and indeed Alpha won’t factor it.
To be honest I’m sort of surprised that Alpha is happy to factor 4678946132165798721321, I’d have thought that that was already too large.
The reason nobody will bother is that it’s just one 200 digit number among another 10^200 similar numbers. Even if you care about one of them enough to ask Wolfram Alpha, it’s vanishingly unlikely to be that particular one.
Technically it is harder, since there are more digits; apart from the additional work involved this also makes more opportunities for mistakes. In addition, of course, the computer at the other end is going to have to do more work.