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Teorema de Euclides: primos infinitos

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Teorema de Euclides: primos infinitos

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Primos sin fin

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diego araya
diego araya
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Teorema de Euclides: primos infinitos
 

Teorema de Euclides: primos infinitosOnline version

Primos sin fin

by diego araya
1

¿Qué afirma el teorema de Euclides sobre los primos?

2

¿Qué se construye para la demostración clásica?

3

¿Qué se demuestra al analizar P respecto a los primos de la lista?

4

¿Qué tipo de contradicción se usa en la prueba?

5

Si un primo no está en la lista dada, ¿qué debe ocurrir?

6

¿Qué dice el teorema acerca de la existencia de primos grandes?

7

¿El teorema proporciona una lista de todos los primos?

8

¿Qué opción describe mejor P en la demostración?

9

¿Qué concepto se utiliza para concluir la infinitud?

10

¿Qué garantiza el teorema sobre la distribución de primos?

Explicación

Explica que no hay un último primo; siempre hay uno más grande.

Se forma P = p1*p2*...*pk + 1 para generar un nuevo candidato.

P deja remainder 1 al dividirse entre cada p_i de la lista.

Asume finitud de primos y llega a un número que contradice esa suposición.

Un primo no en la lista debe aparecer como divisor de P para justificar su existencia.

Implica que no hay un último primo; siempre hay uno más grande.

La prueba demuestra infinitud sin computar todos los primos.

P = p1*p2*...*pk + 1 crea un número que no comparte factor con la lista.

El hecho de que P no es múltiplo de ninguno de los primos conocidos genera contradicción.

El teorema no da distribución exacta, solo infinitud.

 
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