What Is the Product of Primes for the Integer 23?

PsychonautQQ
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Homework Statement


My textbook says any integer greater than 1 is a product of primes. Wouldn't that mean that there are no prime numbers? What is the product of primes that create the integer 23?


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The Attempt at a Solution

 
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PsychonautQQ said:

Homework Statement


My textbook says any integer greater than 1 is a product of primes. Wouldn't that mean that there are no prime numbers? What is the product of primes that create the integer 23?


Homework Equations





The Attempt at a Solution


No. 23, for example, is prime. But it is true that any number that is not prime is a product of primes.
 
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PsychonautQQ said:
any integer greater than 1 is a product of primes

In this case, the plural of the word "primes" can also be singular.
 
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Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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