mersenneforum.org "Not Mersenne" formula
 Register FAQ Search Today's Posts Mark Forums Read

 2022-01-31, 01:56 #12 a1call     "Rashid Naimi" Oct 2015 Remote to Here/There 2·11·103 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, 14:30   #13
Dr Sardonicus

Feb 2017
Nowhere

22·1,459 Posts

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$

Last fiddled with by Dr Sardonicus on 2022-01-31 at 14:34 Reason: gifnix optsy

 2022-01-31, 16:23 #14 kriesel     "TF79LL86GIMPS96gpu17" Mar 2017 US midwest 147038 Posts For almost any real a, a0=1. Why should it be different for a=0? Limit as a->0 from above of aa is? Last fiddled with by kriesel on 2022-01-31 at 16:24
2022-01-31, 16:52   #15
slandrum

Jan 2021
California

22×107 Posts

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 aa is?
For almost any real a, 0a=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.

Last fiddled with by slandrum on 2022-01-31 at 16:54

 2022-01-31, 17:10 #16 paulunderwood     Sep 2002 Database er0rr 11×383 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
2022-01-31, 19:14   #17
ZFR

Feb 2008
Meath, Ireland

3×61 Posts

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

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

(Like vacuous truth?)

 2022-01-31, 20:05 #18 RomanM   Jun 2021 1100102 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?))
 2022-02-01, 13:02 #19 Technical   13×691 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
2022-02-01, 17:30   #20
Batalov

"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

7×1,409 Posts

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.

 Similar Threads Thread Thread Starter Forum Replies Last Post samuel Miscellaneous Math 247 2019-08-05 23:27 Lan Miscellaneous Math 24 2019-06-09 12:58 Godzilla Miscellaneous Math 5 2019-03-12 09:34 MathDoggy Miscellaneous Math 13 2019-03-03 17:11 hoca Math 7 2007-03-05 17:41

All times are UTC. The time now is 19:54.

Tue Jul 5 19:54:35 UTC 2022 up 82 days, 17:55, 1 user, load averages: 1.31, 1.23, 1.23