Math Awareness DayCollege of the Siskiyous

April 21, 2010

In collaboration with:COS Mathematics Department

Prizes sponsored by: MESA

COS Bookstore

Today’s activities

1. Prime Jump! Or Indoor activity

2. Digits of Pi memorization contest

3. Math Charades (if time allows)

4. TRIVIA!

Math Awareness Month is April 2010!

• http://www.mathaware.org• The theme for this year is Math and Sports.• PRIME JUMP!• A prime number is any number, greater than 1,

that is only divisible by 1 and itself.• 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37,…• A composite number is divisible by numbers

other than 1 and itself• 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22,…

Rules for PRIME JUMP

• 11 contestants compete in the order called.• Each contestant takes one turn per round.• You may only step on prime numbers. If you

step on a composite, you are disqualified!• Elimination. After the first round of jumping,

primes already used will be crossed off. This will continue each round.

• The very last person to completely make it through each round without getting disqualified wins a prize!

Indoor gameConsecutive Prime Circles

• Gather into 3 circles at least 11 people per circle

• The first person chosen by a judge names the number 2. Moving to the left, each person names the next prime number.

• If you name a composite, you are out!• The last person in each group remaining

wins a prize! (if you exceed 1,000 everyone left wins a prize!)

An application of Prime numbers!Internet security using credit cards

• May I borrow a credit card from someone?

• My credit card number is 1234 5678 9876 5432

• Encrypt EACH four digit sequence separately.

1234 5678 9876 5432

Encrypting the credit card #using RSA Encryption

• Pick 3 prime numbers (13, 43, 59) very specifically chosen (math involved!)

• Take the first four digits, 1234. Raise this number to the 13th power (A prime power!)

• The result of 123413 is

15384984961285911141365976368608720789504

Encrypting the credit card #, cont.

• The number is approx ~ 1.54x1040

• Take the entire 41 digit number and divide it by 43*59 =2537 (a product of two primes!)

• The remainder after division takes place is 2391.

• This is the encrypted message that the other side receives!

Decrypting the message

• In order for the other party to receive your credit card number, they need the decryption number, d.

• First, subtract each prime by 1. 43-1 =42, 59-1 = 58.

• Then, multiply the results together 42*58 = 2436.

• This will be used to find the decryption number, d, used to decipher the message.

The decryption number

• To find the decryption number, first look for the smallest number, d, such that when multiplied by the prime 13 and subtracted by 1, is divisible by 2436.

• In other words, find the smallest number d so that (13d -1)/2436 is a whole number.

• Want to try? Calculators ready? Prize for the first person to get it!

• (long pause)• Hint: it is between 930 and 940. 2436

1)937(13

Finding the decryption number

• d = 937 is the decryption number.

• This is because (13*937)-1 = 12180 and 12180 evenly divides into 2436 (5 times).

• By knowing the decryption number, the credit card number may be decrypted!

Decrypting the message

• Without d, the encrypted message and the product of two primes, the other party cannot decrypt your message!

• To obtain the first four digits of the credit card number:

• Raise 2391937 (how big is this?)• Divide by 2537• The remainder is 1234, the original

number!

By the way, 2391937 is

5358741658392078027245727162446004805176225273454332287945094936874232325483843766872022479682813780900367785822173123534583434492976979021987887110524163574945487563561529000449827277569356457916027601373461365142219595942600196020883817680941784484871127215814319096536731974026971134406955245583171263740825411410629286534673785486822275331174703708591337472497826977825329769682947831316810879824473089814773278707280853529639107869594589376919650392105787217383870283524511174070630824827236608285246472956528934033521049900084086553003944995733500936766618196839261927690044791255888284490476095831913741372024184153981523821338145148228870639576650480181832609469946228807634796956452473272295204636580699686649425565996274719411966412496220279178123648476833962436499686757436569512212801372723991044495839523702724550840202542259831136814215131277059494638103210012997228537051423647501455501900760296683715573544651416309766302736931374090074185653419696873281035654937820990640382020446872064170360400199814698750995185479059249008549354678496513944889126212390750968889940887810796344139477560200315750206968214088014019785700817412946538623451557423891914415137675482830636633568045501585701485555224363686259614782456108840068618263369828605319481810903759481032695625612850079473077689940180166787241879802781109364448667418447083154009602594607119705622717479194014386036885590900944577148357674618274828605432182540318898381467393149048856066123632449446888276819738714853459701889923427944409162824299500588465113741441600203860176180358761063269481023648081440968537879138320680654825959975261517712805705209157977223006777221884676735126360790518667665060656489971102449170591691704420984409314174372784445041131160206211883150539135708033187096925469577010173744562946432821545045972353847409168618644947064646644314853782405151228150429369770548978572533753529003676695416538852416674907085723664878569616790728268964029697330729992383242822150205943840572740346336846238615868390939635779227623358120503177421668458867687181349295165786415410630853379000329016218791037047776349553912005835244930035511793057263357484894829044914610637491335915852015645196993411561465813949233673263914865181169502563387510736496621026657377697920971275287179821368535798104357166617119075766111637986117586667643617472351715285629986506348409629557224516149777075482288054798106611676974382415534732462477505762180167658693711606471769805030470596501917854830790665531560895692094341956985829017573611226187586524734875061035604774957187833942680417198127010269807472531255632833538308098088961981634013074457252816146330171367390310967704586857082283000285233999395039885797988281706195982516130525307387144840913549902481275759870214785262585572119123609306364290049929894731043409529901468793380672108560494883119771549298856246791263393751895979672207529611287649927805316797922563515320002387982895697099576929322127497474761264108492251008987954128611794633129067022484296232247217951904682383100298053969768788143604661909131888706949765509362420292443477732909130245384886277765595019129264747517359960211615180092340559457545858823979899670499563031

Pie and Pi

• Yum!• Dividing the circumference of a circle by its

diameter will give you an approximation of pi.

diameter

ncecircumfere

The first 100 digits of PI

• 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679

• You have 3 mins,14 secs to memorize as many places!

A mnemonic for memorizing the first 24 digits of Pi.

• How I want a drink, alcoholic of course, after the heavy lectures involving quantum mechanics. All of thy geometry, Herr Planck, is fairly hard...:

• Count the # of letters in each word

• 3.14159265358979323846264...

Math Charades

• 3 contestants, 3 teams

• Each contestant gets a card with a math-related theme on it.

• Without speaking or spelling out the word. The team will try to guess what the person is acting out.

• The first team to guess correctly wins their contestant a prize.

Trivia (first person to raise their hand and answer wins a prize!)

• What type of encryption was used today to secure my credit card number?

• What are the last names of the people who came up with the RSA Encryption algorithm?

• What three things do you need to decrypt a message using RSA?

Trivia part 2

• What two parts of a circle and in what order do you divide to find the number pi?

• What is the world record for the number of digits of PI memorized?

Answers

• What type of encryption was used today to secure my credit card number?– RSA Encryption

• What are the last names of the people who came up with the RSA Encryption algorithm?– Rivest, Shamir and Adelman

• What three things do you need to decrypt a message using RSA?– The decryption number, the encrypted message and

the product of two primes.

• What two parts of a circle and in what order do you divide to find the number PI?– Circumference/Diameter

• What is the world record for the number of digits of PI memorized?– Lu Chao, China memorized 67,890 digits