What is your favorite hypothesis that seems to hold only if you consider the first, say, million numbers?

“All numbers are smaller than 1,000,000”
I believe you have to go past 10^16 to find counter-example(s) to the Mertens conjecture.
The Pólya conjecture. For any N, write each number from 1 to N as a product of primes. Put all of the numbers that are written as a product of an odd number of primes on the left and put all the numbers that are written as a product of an even number of primes on the right. The conjecture states that the numbers on the right will never outnumber the numbers on the left. The smallest counterexample is N = 906,150,257.
by
Euler’s sum of powers conjecture
Numbers have no more than five digits
by
Borwein integrals !
Hypothesis : All natural numbers are less than a million
All numbers are less than or equal to 1 million
"All positive integers are less than 1000000" only holds up to about the millionth case.
The 3x+1 problem only has the 4-2-1 loop

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