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1. Use the digits 2, 4, 5, and 7 each once to create two prime numbers. What is the smallest possible product of two prime numbers created from these digits?

2. Most non-negative integers can be written as the sum of a prime number plus a perfect square. For instance, 21 can be written as  What is the smallest number greater than 1 which cannot be expressed in this way?

3. How many sets of 3 primes sum to 20?

4. Find the smallest positive integer with the same number of positive divisors as 9775.

 

THX FOR ALL YOUR HELP!!

 Oct 6, 2019
 #1
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1 )    457 x 2 =914

 

3 )    2+5+13 =20     and       2+7+11 =20

 

4 )   60

 Oct 6, 2019
 #2
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2 = 2+0

3 = 3+0

4 = 3+1

5 = 5+0

6 = 2+4, 5+1

7 = 3+4

8 = 7+1

9 = 7+2

 

10 = 

2+8 X

3+7 X

5+5 X

7+3 X

 

10 is the smallest number > 1 that can't be expressed as stated.

 Oct 6, 2019

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