Genady

Yes! +1.

I disagree. Computational methods are math by itself which are applied to math of the physical theories. E.g., FEM.

In fact, simulations are MORE math. Given equations that cannot be solved exactly, developing a working method for solving them numerically is a nontrivial math itself.

If I'm not mistaken, there is an error in the last part:

Scientists discover the world’s largest coral — so big it can be seen from space | CNN This is cool, but the following video in the story made me, a retired SCUBA instructor, cringe. SCUBA divers / marine biologists, do you see what is wrong with this picture? https://media.cnn.com/api/v1/loops/stellar/prod/video-world-s-largest-coral-4.mp4?c=original

Multiplication example. Take 13 jars. Put 19 beans in each jar. Take out all the beans and count them. The number, 247, is a result of multiplying 13 by 19. Inverse multiplication example. Take 247 beans. Put them one-by-one in 13 jars, one bean in each jar at a time, until all the beans are in the jars. Take out beans from one of the jars and count them. The number, 19, is a result of the inverse operation (aka dividing 247 by 13.)

I think that the fruit tree metaphor is wrong. It assumes that physicists are standing now on the same ground level as Einstein, Heisenberg, Feynman et al were standing on, while the branches are farther away. It is not so. The branches reached by Einstein, Heisenberg, Feynman et al are the new ground level, and the "higher" branches are not necessarily farther away.

AFAIK, Galileo worked freely and productively for about two decades (and even under Pope's patronage) until the Inquisition decided to stop it.

Yes. It is easy to show that such a polynomial does not exist for not integer n. So, yes, the question can be clarified: n and all coefficients of the polynomial being integers. It is not needed for this puzzle. Here is almost complete proof:

I mean that. +1. As a bonus exercise, prove that it is the only answer.

Including GR, AFAIK.

... while producing all his great works long before that.

Find a polynomial function, f(n) whose output is a prime number for any input number, n.

This reminds me of the passage from Feynman's "QED: The Strange Theory of Light and Matter":

It is a point. A point at a different time or in a different place, is a different point.

The length, width, and hight are spatial intervals rather than spatial points. Similarly, "time it takes to boil an egg" is a temporal interval rather than a point in time. The spacetime concept does not combine such intervals. It combines the points. For example, "7 pm on the corner of 5th Avenue and 24th Street in NYC" is a point in spacetime.

At least, our votes have helped one D Senator and one D Representative.

I understand your frustration, but you don't think that such papers hinder a progress of foundational physics, do you?

+1. However, the "take some time" part can be accomplished in three steps, like this: Is this what you've meant?

That is, 48 + 68 + 98.

Oh. I found the first one with pen and paper.

Thank you. I don't have any progress to report on my part, but would ask you to clarify your answers somewhat (to get a hint, maybe): Do you mean 3-digits and 6-digits prime numbers? There are more than these three factors, aren't there? (Only these three fall short of 2484.) Or, do you mean these three just repeat many times in the factorization?

What do you mean? Number of digits?

I got one factor. 17.