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This ppt. is about Significance of Prime Numbers in Nature and Islam.

Dr. Farhana Shaheen

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- 1. SIGNIFICANCE OF PRIME NUMBERS IN ISLAM Dr. Farhana Shaheen Yanbu University College
- 2. STORY OF NUMBERS• The story of numbers begins with Natural numbers = {1, 2, 3, 4, 5, ……} initiated by counting, Whole Numbers, Integers, Real Numbers, and ends up to the set of Complex Numbers, the largest existing numbers, comprising of Real and Imaginary numbers (x+iy, where , x, y are real). 2
- 3. 3
- 4. Special Subsets of Integers• Set of Integers Z = {….-3,-2,-1, 0, 1, 2,..} a subset of Real Numbers, has many specific subsets like: Even Numbers: 0, 2, 4, 6, 8, … Odd Numbers: 1, 3, 5, 7, 9, … Prime Numbers, Composite Numbers, Fibonacci Numbers, Lucas Numbers, etc. 4
- 5. What are Prime Numbers• Numbers which have only two divisors (factors), 1 and the number itself.• A prime number can be divided, without a remainder, only by itself and by 1.• For example, the only factors of 17 are 17 and 1.• 2, 3, 5, 7, 11, 13, 17, 19, 23, … are all primes.• A prime number must be a whole number greater than 1. 5
- 6. Composite Numbers• A number which has divisors other than 1 and itself are called Composite Numbers.• Example: 15= 1x3x5• A composite number is defined as any number, greater than 1, that is not prime.• Every composite number can be written as a product of primes. For example: 54= 2.3.3.3 Except for 0 and 1, a number is either a prime number or a composite number. 6
- 7. Prime factorization of number 48 using Tree Diagram 7
- 8. Properties of Primes• Number 1 is neither a prime nor a composite number.• Number 2 is the ONLY Even prime number and the smallest prime too.• All other prime numbers are odd.• All prime numbers are positive numbers.• Prime numbers are infinite. 8
- 9. How to find Prime Numbers List of Prime Numbers... 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, . ..• We can use Sieve of Eratosthenes to find Prime Numbers.• To find all primes numbers less than 100, write all numbers starting from 2.• Start with 2, and cancel all multiples of 2.• Then start with 3 and cancel all multiples of 3.• Similarly go for 5, 7, 11. The remaining numbers are all Primes. 9
- 10. Sieve of Eratosthenes 10
- 11. Sieve of Eratosthenes• The sieve of Eratosthenes is one of the most efficient ways to find all of the smaller primes (below 10 million or so). It is named after Eratosthenes of Cyrene, an ancient Greek mathematician; although none of his works have survived, the sieve was described and attributed to Eratosthenes in the Introduction to Arithmetic by Nicomachus. 11
- 12. Primality• The property of being prime is called primality. Verifying the primality of a given number n can be done by trial division. The simplest trial division method tests whether n is a multiple of an integer m between 2 and n . If n is a multiple of any of these integers then it is a composite number, and so not prime; if it is not a multiple of any of these integers then it is prime.• Is the number 2311 a Prime? 12
- 13. Why are Prime numbers fascinating?• Because its easy to understand what they are and hard to prove that they behave any way. And its hard to prove that they behave the way that they should. Its hard to prove that they dont behave the way that they shouldnt. So its like a little puzzle that you look at and you think, "Ahhh, thats easy." But the more you twist it and the more you twist it, it still looks easy, but you never get to the end. You never actually solve the problems. 13
- 14. Where do we find these numbers in our daily life?• In our body?• In nature?• In our daily routine?• In the Islamic rituals that we follow?• Or…In Cryptography???• (Greek kryptos hidden, graphein to write) 14
- 15. Let us see where we find Prime numbers in human body…Are Prime numbers important in our life? 15
- 16. Look at your face:• One head, but two parts of brain• One nose but two nostrils• 2 eyes, 2 ears, 2 cheeks• One mouth but 2 lips 16
- 17. Count your hands, feet, fingers and toes 17
- 18. 2 hands with5 fingerseach2 feet with5toes each 18
- 19. Look at your own hand:• You have ...• 2 hands each of which has• 5 fingers, each of which has• 3 parts separated by• 2 knuckles• Believe it or not, there are 19 bones in each of your hands.• Is this just a coincidence??? 19
- 20. There are three things involved in body movement: 1. The Brain 2. Muscles 3. Skeleton.• 1. The brain sends messages to the muscle to let it know it‟s time for work.• 2. Muscles contract• 3. Pulls bones attached to them. 20
- 21. Number of bones in leg• 30 in one leg. (excluding the hip) 1- femur (thigh bone) 1- patella (knee cap) 1- tibia (shin) 1- fibula 7- tarsals (ankle bones) 5- metatarsals (foot bones) 14- bones of the toes• (all except the great toe have 3 bones) 21
- 22. Number of Ribs in Human Body• 12 pairs of ribs in human body: 7 are directly connected to the Sternum,(center part) 3 are connected through cartilage 2 are floating and not connected. 22
- 23. Size of Ribs• Twelve pairs of flexible, arch like ribs form the lateral portions of the thoracic cage. They increase in length from the first to the seventh and then decrease again from the eighth to the twelfth.(first 7 increasing and last 5 decreasing) 23
- 24. 29 bones in Skull and 29 in Spine• There are 29 bones in the human skull. The cranium has 8; the face has 15 (including the lower jaw); the ears have 6. There are 29 bones in spinal cord. 24
- 25. Fore and hind legs ofquadrupeds are different 25
- 26. PRIMES: ALLAH’SFAVOURITE NUMBERS
- 27. Repeated Three times 27
- 28. 5 Pillar of Islam• The Quran presents them as a framework for worship and a sign of commitment to the faith. They are:• (1) The shahada (Kalma),• (2) Daily prayers (salat),• (3) Alms giving (zakāt),• (4) Fasting during Ramadan (sawm)• (5) The pilgrimage to Makkah (Hajj) at least once in a lifetime. 28
- 29. 5 times prayers 5 times prayers: Fajr, Zohar, Asar, Maghrib, Isha• We recite Subhan Rabbiyal Azeem (3 times/ 7 times) and Subhana Rabbiyal Aala (3 times/ 7 times)• Total number of Fardh Prayers = 17 (prime#) 29
- 30. Reciting Adhkaar-3,7 or 11 times• Most of the Adhkaar that we recite daily, morning or night, or even after each prayer are in Prime numbers.• For example, reciting Allah-o-Akbar and Astaghferullah 3 times after each Fardh Prayers;• Allah humma ajirna minanna‟r 7 times in morning and evening. 30
- 31. 31
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- 33. • 7 days in a week• 7 notes in musical scale 33
- 34. 34
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- 36. 36
- 37. About Seven Skies in Quran• Seven skies is mentioned a lot in the Quran. What is meant by those skies? “And We have made, above you seven tracts; and We are never unmindful of (Our) Creation.”• In seven verses, the number of the skies is mentioned as “seven”; in two of those verses it is stated that the seven skies are in the form of “layers”. (al-Mulk, 67/3; Nuh, 71/15) “Do you not consider how Allah has created seven heavens in layers” (Surah Nuh 71:15) 37
- 38. 7 Heavens: The atmospherehas 7 layers• Today, it is known that the worlds atmosphere consists of different layers that lie on top of each other. Based on the criteria of chemical contents or air temperature, the definitions made have determined the atmosphere of the earth as seven layers. As mentioned in Quran (67:3) “He Who created the seven heavens in layer”. 38
- 39. 7 SeasThe Seven Seas as referenced in MedievalArabian literature:The Persian Gulf ("Sea of Fars")The Gulf of Khambhat ("Sea of Larwi")Bay of Bengal ("Sea of Harkand”)The Strait of Malacca ("Sea of Kalah”) The Singapore Strait ("Sea of Salahit”) The Gulf of Thailand ("Sea of Kardanj”), andThe South China Sea ("Sea of Sanji”). 39
- 40. • The "Arabian seven seas" must also have considered other important seas nearby which were navigated by Arabian and Phoenician seafarers:• the Adriatic Sea• the Arabian Sea• the Black Sea• the Caspian Sea• the Indian Ocean• the Mediterranean Sea• the Red Sea 40
- 41. 7 Oceans 41
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- 43. Ablution (Wudu) has 7 steps• 1.Pour water over hands and wash them thrice• 2. Rinse mouth thrice• 3.Washed nose by putting water in it and then blowing it out• 4.Then wash face thrice• 5. Wash forearms up to the elbows thrice• 6. Pass wet hands over head, both ears and back side of neck• 7. Wash feet up to the ankles thrice 43
- 44. During Umrah Tawaf Ka‟bah: The circumfering of the Kabah 7 times:• 7 rounds of Sai‟ 44
- 45. 7 Requirements of Hajj• (If one neglects a requirement he must compensate for it with a ransom (fidyah) an animal sacrificed in Makkah.• Assuming Ihram from the Meeqat• Staying in Arafaat until the sun has set• Staying in Muzdalifah• Staying in Mina on the nights preceding days of Tashreeq• Stoning the pillars (Rami)• Shaving or cutting the hair• The farewell Tawaf (Al-wada) 45
- 46. Stoning of the Pillars• (On 10th of ZilHajj):• Upon reaching Mina, hajjis hasten to stone the large pillar (Jamratul Aqabah) ONLY, with 7 pebbles (throwing one by one), saying “Allahu Akbar” with each pebble thrown (7 times in total). 46
- 47. What to Sacrifice on Eid-ul- Adha?• Generally, slaughter of goats, sheep, rams, cows, and camels is offered.• It is permissible for seven persons to share the sacrifice of a cow or a camel on the condition that no one‟s share is less than one seventh and their intention is to offer Qurbani (sacrifice). 47
- 48. Ayyam al-Tashreeq• 11th , 12th, 13th of Zilhajj (Days of Drying Meat)• During these 3 days, (Ayyam at-Tashreeq), the pilgrims stone the 3 pillars, from the time period between after zawaal (sun at highest point- no shadow) until the night. They stone all the 3 Jamarats, for which they need 21 (7x3)pebbles per day.• Method: Throw 7 stones (one by one), saying Allahu Akbar each time: first to the small (Jamratul Sughra), then the medium (Jamratul Wusta), and finally, the large (Jamratul Aqabah) pillar. 48
- 49. Hadith about eating 7 Ajwa dates daily:• Sa‟ad told of hearing Allah‟s Messenger say, “He who has a morning meal of seven „ajwa dates will not suffer harm that day through toxins or magic.” (Bukhari, Hadith 5327 and Muslim, Hadith 3814) 49
- 50. People of Cave (Ashaab e Kahaf)• They were 3, and 4th was the dog• They were 5, and 6th was the dog• They were 7, and 8th was the dog (as narrated in Quran) 50
- 51. Number 19 in Quran• The Quran consists of 114 (19 x 6) Suras.• Another mathematical miracle of the Quran is the manner in which the number 19 is numerologically encoded in verses. This number is stressed in the words of the Quran: "There are nineteen (angels) in charge of it." (Quran, 74:30), and is encoded in various places in the Book. 51
- 52. NUMBER 19 in Quran• The first Sura to be revealed, Surat al- Alaq, consists of 19 verses and 285 (19 x 15) letters.• A total of 113 Suras in the Quran start with Bismillah. Sura not to start with one is the ninth, Surat at-Tawba. Surat an-Naml is the only Sura to have two times Bismillah. One of these is at the beginning and the other in verse 30. Counting from Surat at-Tawba, which does not begin with Bismillah, Surat an-Naml follows 19 Suras on. 52
- 53. NUMBER 19 in Quran• The sum of all the occurrences of the name "Allah" in all the verses whose numbers are multiples of 19 (i.e., verses 19, 38, 57, 76, etc.) is 133, or 19 x 7.• The word "Rahman" (All-Merciful) appears 57 (19 x 3) times in the Quran. 53
- 54. • The verse “Which of your Lord‟s marvels can you deny” has been repeated 31 times in Surah Al-Rahman which is a prime number. The sum of all the verses numbers where it is repeated, again gives a prime number 1433, and adding these digits gives again 1+4+3+3=11, a prime. 54
- 55. Prime Numbers in Cryptography• You can search for the importance and significance of Prime numbers in Cryptography, the art of sending secret messages, the establishment of a technical system used in maintaining the secrecy of electronic communications. 55
- 56. 56
- 57. Cryptography: How it works?• A cryptographer starts with plain text such as "ATTACKATDAWN" and produces cipher text such as "OTMMGKLHDTIR." This is encryption. Decryption is the reverse: it produces plain text from cipher text.• Large primes are used in this process of encryption and decryption. 57
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