****************************** MathMagic-10-12 Sample Posting ****************************** PRIMO MATHEMATICS 1) Can you find 2 prime numbers whose sum is prime? 2) Can you find 2 prime numbers whose product is prime? 3) What is the smallest positive number divisible by 1, 2, 3, 4, 5, and 6. 4) What is the smallest non-negative number divisible by 1, 2, 3, 4, 5, and 6. 5) What is the smallest number divisible by 1, 2, 3, 4, 5, and 6. 6) The numbers 24, 25, 26, 27, 28 is a string of 5 consecutive composite numbers. Can you find another string of five conse- cutive composite numbers less than 100. 7) What is the longest string of consecutive composites less than 200. 8) Twin primes are 2 primes that differ by 2. List all twin primes less than 30. 9) A Mersenne prime is any prime number of the form 2^p - 1, where p is prime. Find 3 mersenne primes. Is 199 a mersenne prime? Is 63 a mersenne prime? 10)If a prime is mersenne, then it can be used to produce a perfect number. A perfect number is any whole number whose sum of proper divisors is equal to the number itself. If 2^p - 1 is prime then (2^p - 1)(2^(p-1)) is a perfect number. Find at least 3 perfect numbers and check. 11)Find the sum of the reciprocals of ALL the divisors of each perfect number in #10. What do you notice? ****************************** MathMagic-10-12 Sample posting ****************************** STATISTICALLY SPEAKING... 1) Find 3 numbers whose mode is 8 and mean is 10. What is the median of these 3 numbers? 2) Find the mean median and mode X Value | 2 3 4 5 ----------|-------------------- Frequency | 4 2 5 1 3) Find the mean median and mode X Value | 2 3 4 5 ----------|--------------------- Frequency | 40 20 50 10 4) Based on your results, what can you determine regarding the mean median and mode for the distributions above? 5) If the distribution continues proportionally as above, what is the frequency distribution for n=180 observations? 6) A probability mass function (PMF) expresses the frequency of each observation as a probability rather than a frequency. Write the probability mass function. Assume that only 2, 3, 4, and 5 are possible. 7) Use your PMF in #6 to find each probability: A) x<4 B) x>4 C) x=4 D) x is even E) Which is more likely: x is even or x is odd? F) The odds of an occurrence = probability it occurs divided by probability it does not occur. Find the odds of "x is 3." ------------------------------------------------------------------ The above are samples, and are intended to be a guide for generat- ing discussions that will lead to solutions. ------------------------------------------------------------------