d.) Find the second perfect number using the formula (2P-1)(2P – 1)and the next prime number for P. (Do not use P = 4, since 4 is not prime). TIP: when you are done, you might do a web search for perfect numbers to see if you are right. e.) Show how you know this new number is perfect by showing what the proper divisors add up to. Each f.) Find the third perfect number using the formula (2º-1)(2° – 1) and the next prime number for P. Show your work, not just your answer.

How many multiples of 5 are there between 199 and 1,198? Hint: an = a₁ + d(n-1), where a₁ is the first term and d is the common difference. O 142 O 128 O 144 O 200

(a) At a glance, determine the digit d so that 64,275,67d is divisible by 4. Is there more than one answer? (b) Can you choose the digit d so that 64,275,67d is divisible by 8 and not 16? O A. The digit d can be 6. Oc. The digit d can be 4 or 8. B. The digit d can be 0, 2, or 6. D. The digit d can be 8. O E. The digit d can be 2 or 6. OF. The digit d can be 0. O G. The digit d can be 2. O H. The digit d can be 4. O 1. The digit d can be 0, 2, 4, 6, or 8. O J. The digit d can be 0, 4, or 8.

How many twin primes are there where both primes are less than or equal to 31? Number of twin primes:

2. Use the formula indicated to determine the prime number generated for the given value of n. P= n²-79n+ 1601; for n = 42

Consider the list of numbers: 2n-1, where n first equals 2, then 3, 4, 5,6,…What is the smallest value of n for which 2n -1 is not a prime number.  Show all your work.

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n 3. For each of the numbers in (a) through (d), determine whether it is a prime number. If it is not a prime number, factor the number into a product of prime numbers. 6. F y 3- a. 8303 b. 3719 fa с. 3721 holhivi la d. 80,000