Question: 11. The numbers 13 and 31 are reversed prime; the digits are reversed.
Give two pairs of reversed prime
12. Give two consecutive numbers that are both prime.
13. Give two prime numbers whose sum is prime. Give some possible pairs of numbers.
Write the answers as addition sentences.
14. Give two prime numbers whose sum is odd. Give some possible pairs of numbers. Write the answers as addition sentences.
Let's Take a Breakthrough
Express each even number as a sum of two primes.
1. 14 = 11 + 3
2. 24 = 11 + 13, 7 + 17, 5 + 19
3. 38 = ____ + ____
Express each odd number as a sum of two primes.
4. 21 = ____ + ____
5. 45 = ____ + ____
6. 39 = ____ + ____
1. **Problem:** Find two pairs of reversed prime numbers.
**Step 1:** Understand reversed primes are pairs like $13$ and $31$ where digits are reversed and both numbers are prime.
**Step 2:** Examples:
- $17$ and $71$ (both prime)
- $37$ and $73$ (both prime)
**Answer:** Two pairs of reversed primes are $17 + 71$ and $37 + 73$.
2. **Problem:** Find two consecutive numbers that are both prime.
**Step 1:** Consecutive numbers differ by $1$. Except for $2$ and $3$, no two consecutive integers are both prime because one will be even.
**Answer:** The only consecutive primes are $2$ and $3$.
3. **Problem:** Find two prime numbers whose sum is prime.
**Step 1:** Sum of two primes is prime only if one of them is $2$ (the only even prime), because sum of two odd primes is even and greater than $2$, hence not prime.
**Step 2:** Examples:
- $2 + 3 = 5$
- $2 + 5 = 7$
**Answer:** Possible pairs are $2 + 3 = 5$ and $2 + 5 = 7$.
4. **Problem:** Find two prime numbers whose sum is odd.
**Step 1:** Sum is odd only if one addend is even and the other is odd.
**Step 2:** Since $2$ is the only even prime, sum is odd if one prime is $2$ and the other is odd prime.
**Step 3:** Examples:
- $2 + 3 = 5$
- $2 + 7 = 9$
**Answer:** Possible pairs are $2 + 3 = 5$ and $2 + 7 = 9$.
5. **Problem:** Express $38$ as sum of two primes.
**Step 1:** Try pairs:
- $5 + 33$ (33 not prime)
- $7 + 31$ (31 prime)
**Answer:** $38 = 7 + 31$.
6. **Problem:** Express $21$ as sum of two primes.
**Step 1:** Try pairs:
- $2 + 19$ (both prime)
- $3 + 18$ (18 not prime)
**Answer:** $21 = 2 + 19$.
7. **Problem:** Express $45$ as sum of two primes.
**Step 1:** Try pairs:
- $2 + 43$ (both prime)
- $3 + 42$ (42 not prime)
**Answer:** $45 = 2 + 43$.
8. **Problem:** Express $39$ as sum of two primes.
**Step 1:** Try pairs:
- $2 + 37$ (both prime)
- $3 + 36$ (36 not prime)
**Answer:** $39 = 2 + 37$.