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.

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}