N\303\272meros Primos & Fatora\303\247\303\243o

0. C\303\263digo:

Nessa primeira parte temos que criar algumas fun\303\247\303\265es que utilizaremos ao longo do m\303\263dulo. O c\303\263digo delas segue abaixo:

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JSFH

1. Pedras Fundamentais:

O maple possui um comando para fatorar qualquer numero. O comando ifactor( ) pode fatorar qualquer numero que seja colocado dentro dos parenteses. Confira os exemplos a seguir:

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KiotSSFHNiI2IyIiI0YnLUYkNiMiIiQiIiItRiQ2IyIiJkYnLUYkNiMiIihGKw==

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

LyIjSyokLUkhRzYiNiMiIiMiIiY=

LyIkMCIqKC1JIUc2IjYjIiIkIiIiLUYmNiMiIiZGKi1GJjYjIiIoRio=

LyIkIz4qJi1JIUc2IjYjIiIjIiInLUYmNiMiIiQiIiI=

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

LyIkSyUqJi1JIUc2IjYjIiIjIiIlLUYmNiMiIiRGLQ==

LyIlS1YqKC1JIUc2IjYjIiIjRiktRiY2IyIiJCIiIi1GJjYjIiM+Rik=

LyIlP1YqKC1JIUc2IjYjIiIjIiImLUYmNiMiIiRGLS1GJjYjRioiIiI=

2. O que \303\251 um N\303\272mero Primo?

Quando voc\303\252 tenta fatorar um numero primo no Maple, ele simplesmente retorna o n\303\272mero, j\303\241 que n\303\243o \303\251 possivel fator\303\241-lo:

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No caso de numeros compostos, o Maple retorna os numeros primos que os comp\303\265em:

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3. Quantos Primos Existem? E qual \303\251 o maior N\303\272mero Primo?

Aqui usamos uma fun\303\247\303\243o que criamos anteriormente. Ela ir\303\241 recolher alguns n\303\272meros primos. Veja o exemplo de suas aplica\303\247\303\265es:

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Aqui temos o comando ithprime( ) que retorna o i-\303\251simo numero que voc\303\252 colocar no parenteses. (Ex: se colocar 3, ele retorna o terceiro, se colocarmos 10, ele retorna o d\303\251cimo, e assim por diante):

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IiRUJg==

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

STMxMDB8XXd8ZXZ+cHJpbW9+fF53fGR1fjU0MUc2Ig==

STQyMDB8XXd8ZXZ+cHJpbW9+fF53fGR1fjEyMjNHNiI=

STQzMDB8XXd8ZXZ+cHJpbW9+fF53fGR1fjE5ODdHNiI=

STQ0MDB8XXd8ZXZ+cHJpbW9+fF53fGR1fjI3NDFHNiI=

STQ1MDB8XXd8ZXZ+cHJpbW9+fF53fGR1fjM1NzFHNiI=

STQ2MDB8XXd8ZXZ+cHJpbW9+fF53fGR1fjQ0MDlHNiI=

STQ3MDB8XXd8ZXZ+cHJpbW9+fF53fGR1fjUyNzlHNiI=

STQ4MDB8XXd8ZXZ+cHJpbW9+fF53fGR1fjYxMzNHNiI=

STQ5MDB8XXd8ZXZ+cHJpbW9+fF53fGR1fjY5OTdHNiI=

STUxMDAwfF13fGV2fnByaW1vfnxed3xkdX43OTE5RzYi

STUxMTAwfF13fGV2fnByaW1vfnxed3xkdX44ODMxRzYi

STUxMjAwfF13fGV2fnByaW1vfnxed3xkdX45NzMzRzYi

STYxMzAwfF13fGV2fnByaW1vfnxed3xkdX4xMDY1N0c2Ig==

STYxNDAwfF13fGV2fnByaW1vfnxed3xkdX4xMTY1N0c2Ig==

STYxNTAwfF13fGV2fnByaW1vfnxed3xkdX4xMjU1M0c2Ig==

STYxNjAwfF13fGV2fnByaW1vfnxed3xkdX4xMzQ5OUc2Ig==

STYxNzAwfF13fGV2fnByaW1vfnxed3xkdX4xNDUxOUc2Ig==

STYxODAwfF13fGV2fnByaW1vfnxed3xkdX4xNTQwMUc2Ig==

STYxOTAwfF13fGV2fnByaW1vfnxed3xkdX4xNjM4MUc2Ig==

STYyMDAwfF13fGV2fnByaW1vfnxed3xkdX4xNzM4OUc2Ig==

Aqui usamos outra fun\303\247\303\243o que criamos. Ela ira mostrar que os n\303\272meros primos s\303\243o infinitos:

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IiIj

IiIk

IiIm

IiIo

SSJ+RzYi

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SWVuU2V+YWRpY2lvbmFybW9zfnVtfmF+ZXNzZX5wcm9kdXRvLH5ufF53fF52c350ZW1vc35vfm51bWVyb34yMTFHNiI=

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IiIj

IiIk

IiIm

IiIo

IiM2

IiM4

IiM8

SSJ+RzYi

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SWdvU2V+Mzd+KE9+fjEyfF13fGV2KnByaW1vKX58Xnd8ZHV+b35tYWlvcn5ufF53fGV2bWVyb35wcmltbyx+ZW50fF53fF51b35vc35wcmltb3N+cG9kZW1+c2VyfjpHNiI=

IiIj

IiIk

IiIm

IiIo

IiM2

IiM4

IiM8

IiM+

IiNC

IiNI

IiNK

IiNQ

SSJ+RzYi

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SV9vU2V+YWRpY2lvbmFybW9zfnVtfmF+ZXNzZX5wcm9kdXRvLH5ufF53fF52c350ZW1vc35vfm51bWVyb343NDIwNzM4MTM0ODExRzYi

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LyIuNls4UTJVKCooLUkhRzYiNiMiJCI9IiIiLUYmNiMiJ0BrbkYqLUYmNiMiJjYxJ0Yq

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbW9HRiQ2LVEhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkMtRiM2JS1JI21pR0YkNiVRLUxhcmdlc3RQcmltZUYnLyUnaXRhbGljR1EldHJ1ZUYnL0YwUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUkjbW5HRiQ2JFEjNTNGJ0YvRi9GL0YvRisvJStleGVjdXRhYmxlR0Y0Ri8=

SWdvU2V+NTN+KE9+fjE2fF13fGV2KnByaW1vKX58Xnd8ZHV+b35tYWlvcn5ufF53fGV2bWVyb35wcmltbyx+ZW50fF53fF51b35vc35wcmltb3N+cG9kZW1+c2VyfjpHNiI=

IiIj

IiIk

IiIm

IiIo

IiM2

IiM4

IiM8

IiM+

IiNC

IiNI

IiNK

IiNQ

IiNU

IiNW

IiNa

IiNg

SSJ+RzYi

SV9vT35wcm9kdXRvc35kZXNzZXN+bnxed3xldm1lcm9zfnByaW1vc35jb25oZWNpZG9zfnxed3xkdX4zMjU4OTE1ODQ3NzE5MDA0NDczMEc2Ig==

SWZvU2V+YWRpY2lvbmFybW9zfnVtfmF+ZXNzZX5wcm9kdXRvLH5ufF53fF52c350ZW1vc35vfm51bWVyb34zMjU4OTE1ODQ3NzE5MDA0NDczMUc2Ig==

SVxvMzI1ODkxNTg0NzcxOTAwNDQ3MzF+bnxed3xedW9+fF53fGR1fnByaW1vLH5tYXN+aXN0b35wb3NzdWl+bm92b3N+cHJpbW9zLkc2Ig==

LyI1SlovIT54JWUiKmVLKiotSSFHNiI2IyIjdCIiIi1GJjYjIiRSIkYqLUYmNiMiJHQiRiotRiY2IyIvLC4nPXdrJj1GKg==

Aqui segue o c\303\241lculo sobre a quantidade de p\303\241ginas necess\303\241rias para escrever um n\303\272mero de 300.000 d\303\255gitos:

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

ImVxKysrKysrKysrKysrKysrKysrKysrKysrKysrKysrKysrKysrKysrKysrKysrKysrKysrKzU=

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

L0k1bnxed3xldm1lcm9zfmRlfmR8Xnd8aHVnaXRvc0c2IiInKytJ

L0kzbnxed3xldm1lcm9zfmRlfmxpbmhhc0c2Ii8sJEk1bnxed3xldm1lcm9zfmRlfmR8Xnd8aHVnaXRvc0dGJCMiIiIiJDAiIyImKysjIiIo

L0k1bnxed3xldm1lcm9zfmRlfnB8Xnd8XHVnaW5hc0c2Ii8sJEkzbnxed3xldm1lcm9zfmRlfmxpbmhhc0dGJCMiIiIiI10vLCRJNW58Xnd8ZXZtZXJvc35kZX5kfF53fGh1Z2l0b3NHRiQjRikiJV1fIyIkKyUiIig=

JSFH

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

JCIrJVwwWFwmISIp

4. Crivo de Erat\303\263stenes:

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEzQ3Jpdm9kZUVyYXN0b3RlbmVzRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiUtSSNtbkdGJDYkUSM0MEYnL0YzUSdub3JtYWxGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnRj5GPkZARj4=

SVBBYmFpeG9+ZXN0fF53fF51b35vc35pbnRlaXJvc35hfnBhcnRpcn5kb34yfmF0fF53fGR1fjQ2RzYi

SSJ+RzYi

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyNLSSdtYXRyaXhHRiU2IzcnNysiIiMiIiQiIiUiIiYiIiciIigiIikiIioiIzU3KyIjNiIjNyIjOCIjOSIjOiIjOyIjPCIjPSIjPjcrIiM/IiNAIiNBIiNCIiNDIiNEIiNFIiNGIiNHNysiI0giI0kiI0oiI0siI0wiI00iI04iI08iI1A3KyIjUSIjUiIjUyIjVCIjVSIjViIjVyIjWCIjWVEocHByaW50MEYoNyNJIkFHNiMvSSdfbG9jYWxHRiZJMF9uMTg1NDczMzcyMTM3NkdGKA==

SSJ+RzYi

SWZxQWJhaXhvfmVzdHxed3xedW9+b3N+aW50ZWlyb3N+YX5wYXJ0aXJ+ZG9+Mn5hdHxed3xkdX40Nn5kZXBvaXN+ZGV+cmVtb3Zlcn5vc35tfF53fGV2bHRpcGxvc35kZX4yfihleGNldG9+b35wcnxed3xednByaW9+Mn4pRzYi

SSJ+RzYi

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyNLSSdtYXRyaXhHRiU2IzcnNysiIiMiIiRJIn5HRigiIiZGMyIiKEYzIiIqRjM3KyIjNkYzIiM4RjMiIzpGMyIjPEYzIiM+NytGMyIjQEYzIiNCRjMiI0RGMyIjRkYzNysiI0hGMyIjSkYzIiNMRjMiI05GMyIjUDcrRjMiI1JGMyIjVEYzIiNWRjMiI1hGM1EocHByaW50MEYoNyNJIkFHNiMvSSdfbG9jYWxHRiZJMF9uMTg1NDczMzcyMTM3NkdGKA==

SSJ+RzYi

SWZxQWJhaXhvfmVzdHxed3xedW9+b3N+aW50ZWlyb3N+YX5wYXJ0aXJ+ZG9+Mn5hdHxed3xkdX40Nn5kZXBvaXN+ZGV+cmVtb3Zlcn5vc35tfF53fGV2bHRpcGxvc35kZX4zfihleGNldG9+b35wcnxed3xednByaW9+M34pRzYi

SSJ+RzYi

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyNLSSdtYXRyaXhHRiU2IzcnNysiIiMiIiRJIn5HRigiIiZGMyIiKEYzRjNGMzcrIiM2RjMiIzhGM0YzRjMiIzxGMyIjPjcrRjNGM0YzIiNCRjMiI0RGM0YzRjM3KyIjSEYzIiNKRjNGM0YzIiNORjMiI1A3K0YzRjNGMyIjVEYzIiNWRjNGM0YzUShwcHJpbnQwRig3I0kiQUc2Iy9JJ19sb2NhbEdGJkkwX24xODU0NzMzNzIxMzc2R0Yo

SSJ+RzYi

SV5wT35Dcml2b35kZX5FcmF0fF53fF52c3RlbmVzLkRpen5xdWV+dG9kb35vfm58Xnd8ZXZtZXJvfmRlaXhhZG9+bm9+Y3Jpdm9+fF53fGR1fnVtfm58Xnd8ZXZtZXJvfnByaW1vRzYi

SVVwb3JxdWV+bnxed3xednN+cmVtb3ZlbW9zfnRvZG9zfm9zfm58Xnd8ZXZtZXJvc35jb21wb3N0b3N+ISFHNiI=

JSFH

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEtTnVtYmVyVGhlb3J5RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYmLUYjNiUtRiw2JVEjcGlGJy9GMFEmZmFsc2VGJy9GM1Enbm9ybWFsRicvJStleGVjdXRhYmxlR0Y+Rj9GPy8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJy1GNjYkLUYjNiUtSSNtbkdGJDYkUSM0NkYnRj9GQUY/Rj9GQUY/

IiM5

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEzQ3Jpdm9kZUVyYXN0b3RlbmVzRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiUtSSNtbkdGJDYkUSQxOTlGJy9GM1Enbm9ybWFsRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJ0Y+Rj5GQEY+

SVFBYmFpeG9+ZXN0fF53fF51b35vc35pbnRlaXJvc35hfnBhcnRpcn5kb34yfmF0fF53fGR1fjIwMUc2Ig==

SSJ+RzYi

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

SSJ+RzYi

SWdxQWJhaXhvfmVzdHxed3xedW9+b3N+aW50ZWlyb3N+YX5wYXJ0aXJ+ZG9+Mn5hdHxed3xkdX4yMDF+ZGVwb2lzfmRlfnJlbW92ZXJ+b3N+bXxed3xldmx0aXBsb3N+ZGV+Mn4oZXhjZXRvfm9+cHJ8Xnd8XnZwcmlvfjJ+KUc2Ig==

SSJ+RzYi

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

SSJ+RzYi

SWdxQWJhaXhvfmVzdHxed3xedW9+b3N+aW50ZWlyb3N+YX5wYXJ0aXJ+ZG9+Mn5hdHxed3xkdX4yMDF+ZGVwb2lzfmRlfnJlbW92ZXJ+b3N+bXxed3xldmx0aXBsb3N+ZGV+M34oZXhjZXRvfm9+cHJ8Xnd8XnZwcmlvfjN+KUc2Ig==

SSJ+RzYi

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

SSJ+RzYi

SWdxQWJhaXhvfmVzdHxed3xedW9+b3N+aW50ZWlyb3N+YX5wYXJ0aXJ+ZG9+Mn5hdHxed3xkdX4yMDF+ZGVwb2lzfmRlfnJlbW92ZXJ+b3N+bXxed3xldmx0aXBsb3N+ZGV+NX4oZXhjZXRvfm9+cHJ8Xnd8XnZwcmlvfjV+KUc2Ig==

SSJ+RzYi

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SSJ+RzYi

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SSJ+RzYi

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JSFH

IiNZ

Aqui iremos usar um comando para criar um gr\303\241fico que mostra a distribui\303\247\303\243o dos n\303\272meros primos:

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Nesse gr\303\241fico iremos comparar o gr\303\241fico anterior com a conjectura de Gauss:

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LyIlSkMqKC1JIUc2IjYjIiM2IiIiLUYmNiMiIzhGKi1GJjYjIiM8Rio=

Aqui iremos tentar encontrar a raiz quadrada de alguns n\303\272meros:

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzY1LUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLUkjbWlHRiQ2JVErRmluZFNxdWFyZUYnLyUnaXRhbGljR1EldHJ1ZUYnL0YwUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUkjbW5HRiQ2JFEjNDJGJ0YvLyUrZXhlY3V0YWJsZUdGNEYvRi8tRiw2LVEiO0YnRi9GMi9GNkZMRjdGOUY7Rj1GP0ZBL0ZFUSwwLjI3Nzc3NzhlbUYnLUknbXNwYWNlR0YkNiYvJSdoZWlnaHRHUSYwLjBleEYnLyUmd2lkdGhHRkMvJSZkZXB0aEdGX28vJSpsaW5lYnJlYWtHUShuZXdsaW5lRictRltvNiZGXW9GYG9GYm8vRmVvUSVhdXRvRidGRi1GUDYkLUYjNiUtRlU2JFEkMzMwRidGL0ZYRi9GL0ZaRmpuRmdvRkYtRlA2JC1GIzYlLUZVNiRRJTI0MzFGJ0YvRlhGL0YvRlpGam5GZ28tRiw2LVEhRidGL0YyRjVGN0Y5RjtGPUY/RkFGREZYRi8=

STg0Mn5ufF53fF51b350ZW1+cmFpen5leGF0YSFHNiI=

STkzMzB+bnxed3xedW9+dGVtfnJhaXp+ZXhhdGEhRzYi

SToyNDMxfm58Xnd8XnVvfnRlbX5yYWl6fmV4YXRhIUc2Ig==

Aqui podemos ver que nenhum n\303\272mero primo possui raiz exata:

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

LyIjPC1JIUc2IjYjRiM=

LyIjVC1JIUc2IjYjRiM=

LyIjKCotSSFHNiI2I0Yj

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

STgxN35ufF53fF51b350ZW1+cmFpen5leGF0YSFHNiI=

STg0MX5ufF53fF51b350ZW1+cmFpen5leGF0YSFHNiI=

STg5N35ufF53fF51b350ZW1+cmFpen5leGF0YSFHNiI=

Identificando os quadrados perfeitos "escondidos" entre os fatores:

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

LyIjNyomLUkhRzYiNiMiIiNGKS1GJjYjIiIkIiIi

LyIkdiQqJi1JIUc2IjYjIiIkIiIiLUYmNiMiIiZGKQ==

LyIjcyomLUkhRzYiNiMiIiMiIiQtRiY2I0YqRik=

LyIkJ28qJi1JIUc2IjYjIiIjIiIiLUYmNiMiIigiIiQ=

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

SUU0fnxed3xkdX5vfm1lbGhvcn5xdWFkcmFkb35xdWV+ZGl2aWRlfjEyRzYi

SUcyNX58Xnd8ZHV+b35tZWxob3J+cXVhZHJhZG9+cXVlfmRpdmlkZX4zNzVHNiI=

SUYzNn58Xnd8ZHV+b35tZWxob3J+cXVhZHJhZG9+cXVlfmRpdmlkZX43Mkc2Ig==

SUc0OX58Xnd8ZHV+b35tZWxob3J+cXVhZHJhZG9+cXVlfmRpdmlkZX42ODZHNiI=

Verificando se os n\303\272meros sem raiz quadrada s\303\243o sempre produtos de n\303\272meros primos distinos:

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

LyIiJyomLUkhRzYiNiMiIiMiIiItRiY2IyIiJEYq

STc2fm58Xnd8XnVvfnRlbX5yYWl6fmV4YXRhIUc2Ig==

Perceba que quando um n\303\272mero possui um primo ao quadrado (ou mais) ele possui raiz quadrada:

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzY1LUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLUkjbW5HRiQ2JFEjMTJGJ0YvRistRiw2LVEiOkYnRi9GMkY1RjdGOUY7Rj1GPy9GQlEsMC4yNzc3Nzc4ZW1GJy9GRUZORistSSNtaUdGJDYlUSIlRicvJSdpdGFsaWNHUSV0cnVlRicvRjBRJ2l0YWxpY0YnRistRiw2LVEiPUYnRi9GMkY1RjdGOUY7Rj1GP0ZNRk9GKy1GUTYlUShpZmFjdG9yRidGVEZXLUkobWZlbmNlZEdGJDYkLUYjNiRGUEYvRi8tRiw2LVEiO0YnRi9GMi9GNkZWRjdGOUY7Rj1GP0ZBRk8tSSdtc3BhY2VHRiQ2Ji8lJ2hlaWdodEdRJjAuMGV4RicvJSZ3aWR0aEdGQy8lJmRlcHRoR0Znby8lKmxpbmVicmVha0dRKG5ld2xpbmVGJy1GY282JkZlb0Zob0Zqby9GXXBRJWF1dG9GJ0YrLUZRNiVRK0ZpbmRTcXVhcmVGJ0ZURlctRmpuNiQtRiM2JC1GUTYlUSMlJUYnRlRGV0YvRi8vJStleGVjdXRhYmxlR0Y0Ri8=

LyIjNyomLUkhRzYiNiMiIiNGKS1GJjYjIiIkIiIi

SUU0fnxed3xkdX5vfm1lbGhvcn5xdWFkcmFkb35xdWV+ZGl2aWRlfjEyRzYi

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LyIjQyomLUkhRzYiNiMiIiMiIiQtRiY2I0YqIiIi

SUU0fnxed3xkdX5vfm1lbGhvcn5xdWFkcmFkb35xdWV+ZGl2aWRlfjI0RzYi

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

LyIjWyomLUkhRzYiNiMiIiMiIiUtRiY2IyIiJCIiIg==

SUU0fnxed3xkdX5vfm1lbGhvcn5xdWFkcmFkb35xdWV+ZGl2aWRlfjQ4RzYi

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