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12 February, 18:56

The fundamental theorem of Arithmetic

The system (E) : The set of all even positive integers

The system (T) : all positive integers congruent to 1 mod 3 1. List the primes in E between 1 and 20. 2. List the primes in E between 21 and 40. 3. List the primes in T between 1 and 30. 4. List the primes in T between 31 and 60.

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  1. 12 February, 21:54
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    1. {2, 3, 5, 7, 11, 13, 17, 19}

    2. {23, 29, 31, 37}

    3. {7, 13, 19}

    4. {37, 43}

    Step-by-step explanation:

    By extension, the set E, is given by:

    E={2, 3, 5, 7, 11, ... }

    In the same way, the set T, is given by:

    T={4, 7, 10, 13, ... } = {t / t is integer and (z-1) it is divisible by 3}

    Let's call E1 the set of primes in E between 1 and 20.

    Let's call E2 the set of primes in E between 21 and 40.

    Let's call T1 the set of primes in T between 1 and 30.

    Let's call T2 the set of primes in T between 31 and 60. Thus,

    E1={2, 3, 5, 7, 11, 13, 17, 19}

    E2={23, 29, 31, 37}

    T1={7, 13, 19}

    T2={37, 43}
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