"Not Mersenne" formula - Page 2

a1call · 2022-01-31, 01:56

The historic justification in the Wikipedia article states:

0^0 = (a-a)^(n-n) = (a-a)^n/(a-a)^n = 1

(a-a)^n is 0 for all real numbers a and defined values n other than 0. This makes the justification based on divide-by-0 which is undefined. Not sure how this can be considered a valid justification. Corrections/insights are appreciated.

Dr Sardonicus · 2022-01-31, 14:30

Quote:

Originally Posted by a1call

The historic justification in the Wikipedia article states:

0^0 = (a-a)^(n-n) = (a-a)^n/(a-a)^n = 1

(a-a)^n is 0 for all real numbers a and defined values n other than 0. This makes the justification based on divide-by-0 which is undefined. Not sure how this can be considered a valid justification. Corrections/insights are appreciated.

0⁰ $\lim_{x\rightarrow 0+}$e^{\frac{1}{x}}$^{x^{2}}\;=\;1$

0⁰ $\lim_{x\rightarrow 0+}$e^{\frac{1}{x}}$^{x}\;=\;e$

0⁰ $\lim_{x\rightarrow 0+}$e^{\frac{1}{x}}$^{\sqrt{x}}\;=\;\infty$

kriesel · 2022-01-31, 16:23

For almost any real a, a⁰=1. Why should it be different for a=0?
Limit as a->0 from above of a^a is?

slandrum · 2022-01-31, 16:52

Quote:

Originally Posted by kriesel

For almost any real a, a⁰=1. Why should it be different for a=0?
Limit as a->0 from above of a^a is?

For almost any real a, 0^a=0. Why should it be any different for a=0?

For 0⁰ you can argue that any results is an answer, same for 0/0.

paulunderwood · 2022-01-31, 17:10

I also draw your attention to: https://en.wikipedia.org/wiki/Zero_t...rent_situation

ZFR · 2022-01-31, 19:14

Quote:

Originally Posted by Dr Sardonicus

Your f(x) is 2 for positive integer x. That's prime, no question.

And large. Let's not forget large. An average of 2 daily lottery jackpots is pretty large I think.

On a bit more serious note, I have a question. If I were to change the formula to:

f(x) = 1^ln(-x) + 0^x!

Would it be correct to say that the above formula also generates only prime numbers for its whole domain?

(Like vacuous truth?)

RomanM · 2022-01-31, 20:05

it is common knowledge that $\lim_{n \rightarrow \infty}\frac{sin(n+1)\phi}{sin(n\phi)}=e^{i\phi}$

its joke, on 50/50 percent)
If every prime number can be associated with a "prime angle" i.e. tg(x) = 7, What are the unique properties of these "prime angles" in the light of their respected prime counterparts?))

2022-02-01, 13:02

Dear Colleague!

What are your views on the following mathematical formula:
C^4 + 3*C^2 + 1
It only contains addition and multiplication, so it's easy to count (exponentiation can be traced back to a series of multiplications).

This formula, when the value of "C" varies from 1 to 10,000, produces 1148 prime numbers.

The first 30 are as follows (C <= 100):

5 29 109 701 2549 4289 10301 21169 84389 161201 281429 812701 1051649 1189189 4106701 5315329 7898909 11326589 14787869 20164589 21395249 24024701 31657501 35170829 37033309 40979201 57312469 65634301 88557509 100030001

Batalov · 2022-02-01, 17:30

Quote:

Originally Posted by Technical

This formula, when the value of "C" varies from 1 to 10,000, produces 1148 prime numbers.

Then it is surely not a formula for prime numbers.
At best, it is a series that happens to have "some" prime numbers in it.

Not interesting at all. In comparison, formula x²-x+41 produces 40 primes for the first 40 values of x, 1..40.

P.S. Creating clones for the banned user is not allowed. You have already created two: Mikloska and Benkoe. Stop doing that or you will be banned by IP.

2022-01-31, 01:56	#12
a1call "Rashid Naimi" Oct 2015 Remote to Here/There 2×11×109 Posts	The historic justification in the Wikipedia article states: 0^0 = (a-a)^(n-n) = (a-a)^n/(a-a)^n = 1 (a-a)^n is 0 for all real numbers a and defined values n other than 0. This makes the justification based on divide-by-0 which is undefined. Not sure how this can be considered a valid justification. Corrections/insights are appreciated. Last fiddled with by a1call on 2022-01-31 at 01:57

2022-01-31, 16:23	#14
kriesel "TF79LL86GIMPS96gpu17" Mar 2017 US midwest 1111010001101₂ Posts	For almost any real a, a⁰=1. Why should it be different for a=0? Limit as a->0 from above of a^a is? Last fiddled with by kriesel on 2022-01-31 at 16:24

2022-01-31, 17:10	#16
paulunderwood Sep 2002 Database er0rr 5×937 Posts	I also draw your attention to: https://en.wikipedia.org/wiki/Zero_t...rent_situation Last fiddled with by paulunderwood on 2022-01-31 at 17:18

2022-02-01, 13:02	#19
Technical 21A0₁₆ Posts	An Alternative Prime Numbers Formula Dear Colleague! What are your views on the following mathematical formula: C^4 + 3*C^2 + 1 It only contains addition and multiplication, so it's easy to count (exponentiation can be traced back to a series of multiplications). This formula, when the value of "C" varies from 1 to 10,000, produces 1148 prime numbers. The first 30 are as follows (C <= 100): 5 29 109 701 2549 4289 10301 21169 84389 161201 281429 812701 1051649 1189189 4106701 5315329 7898909 11326589 14787869 20164589 21395249 24024701 31657501 35170829 37033309 40979201 57312469 65634301 88557509 100030001

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2022-01-31, 20:05	#18
RomanM Jun 2021 3×17 Posts	it is common knowledge that $\lim_{n \rightarrow \infty}\frac{sin(n+1)\phi}{sin(n\phi)}=e^{i\phi}$ its joke, on 50/50 percent) If every prime number can be associated with a "prime angle" i.e. tg(x) = 7, What are the unique properties of these "prime angles" in the light of their respected prime counterparts?))