If [math]P[/math] is a prime number and [math]P_1[/math] is the previous prime number, I've found that [math]P_1-\frac{P_1^2}{P}[/math] tends to an even integer as [math]P[/math] increases. Can this be proved? - Quora
For which of the numbers, from n = 2 to 8, is 2n – 1 a prime? - Sarthaks eConnect | Largest Online Education Community
![number theory - Show that $2^{2^n} = (\prod {p_i^{a_i}}\equiv 2^{n+1 }\alpha_ix_i+1) \mod 2^{2n+2}\implies 2^{n+1} (x_1 \alpha_1 + \dots + x_k\alpha_k ) $ - Mathematics Stack Exchange number theory - Show that $2^{2^n} = (\prod {p_i^{a_i}}\equiv 2^{n+1 }\alpha_ix_i+1) \mod 2^{2n+2}\implies 2^{n+1} (x_1 \alpha_1 + \dots + x_k\alpha_k ) $ - Mathematics Stack Exchange](https://i.stack.imgur.com/IBiS1.png)
number theory - Show that $2^{2^n} = (\prod {p_i^{a_i}}\equiv 2^{n+1 }\alpha_ix_i+1) \mod 2^{2n+2}\implies 2^{n+1} (x_1 \alpha_1 + \dots + x_k\alpha_k ) $ - Mathematics Stack Exchange
![SOLVED: 12. Assuming that pn is the nth prime number, establish each of the following statements: (a) pn > 2n -1 for n > 5. (b) None of the integers Pn = SOLVED: 12. Assuming that pn is the nth prime number, establish each of the following statements: (a) pn > 2n -1 for n > 5. (b) None of the integers Pn =](https://cdn.numerade.com/ask_images/5a40292749814a419a19449acc1724d8.jpg)
SOLVED: 12. Assuming that pn is the nth prime number, establish each of the following statements: (a) pn > 2n -1 for n > 5. (b) None of the integers Pn =
![Set of the Mersenne numbers 2^n - 1 within the first 512 x 512 = 2^18 =... | Download Scientific Diagram Set of the Mersenne numbers 2^n - 1 within the first 512 x 512 = 2^18 =... | Download Scientific Diagram](https://www.researchgate.net/publication/350324828/figure/fig4/AS:1009140981854209@1617609367282/Set-of-the-Mersenne-numbers-2n-1-within-the-first-512-x-512-218-262144-prime.png)
Set of the Mersenne numbers 2^n - 1 within the first 512 x 512 = 2^18 =... | Download Scientific Diagram
![Set of the Mersenne numbers 2^n - 1 within the first 512 x 512 = 2^18 =... | Download Scientific Diagram Set of the Mersenne numbers 2^n - 1 within the first 512 x 512 = 2^18 =... | Download Scientific Diagram](https://www.researchgate.net/publication/350373840/figure/fig2/AS:1009351535898624@1617659567049/Set-of-the-Mersenne-numbers-2n-1-within-the-first-512-x-512-218-262144-prime.png)
Set of the Mersenne numbers 2^n - 1 within the first 512 x 512 = 2^18 =... | Download Scientific Diagram
![SOLVED: Prove that there exists a unique prime number of the form n^2 - 1, where n is an integer and n ≥ 2. SOLVED: Prove that there exists a unique prime number of the form n^2 - 1, where n is an integer and n ≥ 2.](https://cdn.numerade.com/ask_previews/4403145e-c91d-4055-a011-aa0ba6d65c7f_large.jpg)
SOLVED: Prove that there exists a unique prime number of the form n^2 - 1, where n is an integer and n ≥ 2.
![number theory - Are there infinitely many primes of the form $k\cdot 2^n +1$? - Mathematics Stack Exchange number theory - Are there infinitely many primes of the form $k\cdot 2^n +1$? - Mathematics Stack Exchange](https://i.stack.imgur.com/iScA0.jpg)