Chairman Meow
Class IV
Why not?
Let's discuss Mathematics
- Thread starter ParadigmShifter
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Why not?
azzaman333
meh
Because then you can figure out what the next one is.
There's a long history of scientific research being done for its own sake, without thinking about practical applications. Sometimes such research leads to useful results. For example, the Pentium FDIV bug was found by a mathematician performing theoretical calculations that had no real-world value.
Mise
isle of lucy
I'd imagine that the challenge of creating a computer program capable of computing such a large prime would necessitate creating new algorithms or techniques that are applicable elsewhere.
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So, when can we expect the next largest prime number?
Mise
isle of lucy
When they multiply that one by two I'd imagine.
Sent from a phone, apols for any mistakes.
Sent from a phone, apols for any mistakes.
nerdfighter13
Prince of the Universe
But if it is an odd number, it would become an even number.
Mise
isle of lucy
Well you can just add 1 to it afterwards. But anyway, I made a mistake because that number isn't necessarily prime anyway.
Do you know about the Reimann conjecture? It deals with the pattern of primes, sort of. The more and larger primes discovered, the more confidence there is that the conjecture is true. That's still a long way from a proof, but it's still useful.
Edit: many ideas in number theory and other areas of mathematics assume the Reimann conjecture is true.
Although it can't prove Riemann conjecture, it can disprove it, so it does have some meaning.
Though I'd be ready to give good odds that it won't disprove anything (or the next prime found).
Though I'd be ready to give good odds that it won't disprove anything (or the next prime found).
To celebrate Pi day (3/14) identify and/or explain all the instances of pi shown on this clock. Note that the pi symbols on the clock do not always represent 3.14159... .
isn't that cheating? Or, I mean, isn't that a little unfair?
Do you mean that it's unfair that the pi symbol can stand for different concepts?
Yes. An inconsistency
-exp(-i pi) = -(-1)=1 complex exponent
tan(pi/3) = sqrt(3), so the square is 3
The pi_1 is the homotopy group?
The pi in 6 is a product.
[3pi] = [9.xxx]=9 (floor), and the same for 10.
I assume the pi in 11 is somethin like largest prime divisor?
tan(pi/3) = sqrt(3), so the square is 3
The pi_1 is the homotopy group?
The pi in 6 is a product.
[3pi] = [9.xxx]=9 (floor), and the same for 10.
I assume the pi in 11 is somethin like largest prime divisor?
I thought pi_1 was projection.
Yes, the entry for 1 o'clock is based on Euler's identity.
I'll post my proposed solutions in a few days.
Here are my solutions to the Pi clock. There may be a better answer for 7 o'clock.
1 o'clock -- Already noted to follow from Euler's Identity.
2 o'clock -- Follows from Wallis' Product for pi/2.
3 o'clock -- Already noted to follow from the trig identity tan(pi/3) = sqrt(3).
4 o'clock -- Follows from the Leibniz Formula for pi/4.
5 o'clock -- Already noted to involve homotopy groups. In this case, pi1(S1) is the first homotopy group of the 1-sphere. According to this wikipedia entry, it's isomorphic to the additive group of integers Z. Taking the product of 5 copies of Z gives a free abelian group of rank 5.
6 o'clock -- Already noted to equal the product of 1, 2 and 3.
7 o'clock -- Already noted that pi1 stands for projection. Specifically, pi1(x,y) = x. In all the other entries on the clock, the various symbols have their standard meanings. However, I couldn't find a standard meaning for L(7,3). Since L suggests a linear transformation, we'll define L(x,y) to be (-x,y). Using that definition (many others would work just as well), the expression evaluates to 7.
8 o'clock -- Follows from Machin's Formula for pi/4.
9 and 10 o'clock -- Already noted to follow from the definition of the floor function.
11 and 12 o'clock -- In these two entries, pi stands for the prime-counting function. That is, pi(x) equals the number of primes less than or equal to x. It was suggested that pi might stand for the largest prime factor. That works for 11, but not for 12.
Finally, the center of the clock contains a pie chart.
1 o'clock -- Already noted to follow from Euler's Identity.
2 o'clock -- Follows from Wallis' Product for pi/2.
3 o'clock -- Already noted to follow from the trig identity tan(pi/3) = sqrt(3).
4 o'clock -- Follows from the Leibniz Formula for pi/4.
5 o'clock -- Already noted to involve homotopy groups. In this case, pi1(S1) is the first homotopy group of the 1-sphere. According to this wikipedia entry, it's isomorphic to the additive group of integers Z. Taking the product of 5 copies of Z gives a free abelian group of rank 5.
6 o'clock -- Already noted to equal the product of 1, 2 and 3.
7 o'clock -- Already noted that pi1 stands for projection. Specifically, pi1(x,y) = x. In all the other entries on the clock, the various symbols have their standard meanings. However, I couldn't find a standard meaning for L(7,3). Since L suggests a linear transformation, we'll define L(x,y) to be (-x,y). Using that definition (many others would work just as well), the expression evaluates to 7.
8 o'clock -- Follows from Machin's Formula for pi/4.
9 and 10 o'clock -- Already noted to follow from the definition of the floor function.
11 and 12 o'clock -- In these two entries, pi stands for the prime-counting function. That is, pi(x) equals the number of primes less than or equal to x. It was suggested that pi might stand for the largest prime factor. That works for 11, but not for 12.
Finally, the center of the clock contains a pie chart.
I figured 12 pi was not an integer, so it didn't have a largest prime factor, giving 0, which is equal to 12 modulo a clock
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