SIGNIFICANCE OF PRIME
NUMBERS IN ISLAM
Dr. Farhana Shaheen
Yanbu University College
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
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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.
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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.
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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.
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• Prime numbers are said to be the building
block of mathematics, but still there're
many things not known about them.
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Prime factorization of number
48 using Tree Diagram
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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.
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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.
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Sieve of Eratosthenes
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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.
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How many prime numbers are
there?
•
The table below gives you an indication of how many prime numbers
there are in all numbers. For example in the range 0 to 10,000,000
there are 664,579 prime numbers.
Range 0 to ?
No of Primes
% Prime
10
4
40.0%
100
25
25.0%
1,000
168
16.8%
10,000
1,229
12.3%
100,000
9,592
9.6%
1,000,000
78,498
7.8%
10,000,000
664,579
6.6%
100,000,000
5,761,455
5.8%
1,000,000,000
50,847,534
5.1%
10,000,000,000
455,052,511
4.6%
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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?
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Why are Prime numbers
fascinating?
• Because it's easy to understand what they
are and hard to prove that they behave any
way. And it's hard to prove that they behave
the way that they should. It's hard to prove
that they don't behave the way that they
shouldn't. So it's like a little puzzle that you
look at and you think, "Ahhh, that's 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.
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The prime number 73,939,133
• The prime number 73,939,133 has a very strange
property.
If you keep removing a digit from the right hand end
of the number, each of the remaining numbers is
also prime.
It's the largest number known with this property.
Take a
look: 73,939,133 and 73,939,13 and73,939,1 and 73,93
9 and 7,393 and 739 and 73 and7 are all prime!
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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)
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Let us see where we find Prime
numbers in human body…
Are Prime numbers important in
our life?
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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
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Count your hands, feet, fingers
and toes
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2 hands with
5 fingers
each
2 feet with5
toes each
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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???
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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.
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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)
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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.
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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)
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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.
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Fore and hind legs of
quadrupeds are different
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PRIMES: ALLAH’S
FAVOURITE NUMBERS
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Number 3
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32
33
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Repeated Three times
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Drink water in three breaks
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5 Pillar of Islam
• The Qur'an 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.
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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#)
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39
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Reciting Adhkaar3,7 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.
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42
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• 7 days in a week
• 7 notes in musical scale
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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)
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7 Heavens: The atmosphere
has 7 layers
• Today, it is known that the
world's 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
Qur'an (67:3) “He Who created the seven
heavens in layer”.
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• The statement of "seven heavens" is
repeated seven times in Holy Quran.
• "The creation of the heavens (khalq assamawat)" is also repeated seven times.
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7 Seas
The Seven Seas as referenced in Medieval
Arabian 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”), and
The South China Sea ("Sea of Sanji”).
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• Al-Quran• Surat Luqman 31
• Verse 27, Part 21]
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‫ سبعة البحار‬، ‫بحار العالم‬
• The "Arabian seven seas" ‫ سبعة البحار‬، ‫بحار العالم‬must
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
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7 Oceans
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Feast of the Seven Fishes
• The Feast of the Seven Fishes is an Italian
Christmas celebration. Today, it is a feast
that typically consists of seven
different seafood dishes. However,
some Italian-American families have been
known to celebrate with nine, eleven or
thirteen different seafood dishes. This
celebration commemorates the wait for the
midnight birth of the baby Jesus. It is unclear
when the term "Feast of the Seven Fishes"
was popularized.
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• Some people believe that the feast is
named for the Seven hills of Rome that
surround the city.
•
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Seven hills of Rome
• Tradition holds that
the seven hills were
first occupied by
small settlements
and not grouped or
recognized as a city
called Rome.
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H
Haft Sheen (7 S- Food)
• NOU ROUZ the Persian New Year is the only
scientific New Year celebrated in the world
today. Nou Rouz is symbolized by the Nou
Rouz Table with (haft) seven items with S.
• Some call it Haft (seven) Seen and decorate
their table with seven items whose names
start with the letter “Seen” in Persian. All
these items have a positive philosophic
meaning. Others use seven items that start
with the letter “SHeen”. Still others use
seven trays (seenie) and put a variety of
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items.
Age of Reason- 7
• Around the age of 7, children enter the
period of late childhood also called the
“age of reason”. This reasonable age, long
considered like the first step in the big
leagues represents the end of the Oedipal
period and the beginning of a new stage of
logic and understanding of the surrounding
world. This is also the time when their
morality begins.
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The Age of Seven, (Plus
or Minus One).
• "It is not until the age of 7, give or take a
year or so, that your child's conscience
begins to mature enough to guide his/her
actions. It's been called the 'Age of
Reason,' since these children have a
newly internalized sense of right and
wrong. They are no longer focused simply
on not getting caught or displeasing
adults.
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• The Messenger of Allah (PBUH) said:
’Command your children to pray when
they become seven years old, and
enforce them for it (if they refuse to pray)
when they become eleven years old.’
• The Messenger of Allah (PBUH) guided the believers to
encourage their children to start offering their prayers
regularly when they reach seven years of age so that the
children form a habit of offering their prayers unto their
Lord from a very early age.
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• There are many hypotheses for what the
number "7" represents. Seven is the most
repeated number in the Bible and appears
over 700 times.
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Ablution (Wudu) has 7 steps
• 1.Pour water over hands and wash them thrice
• 2. Rinse mouth thrice
• 3.Wash 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
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Prostrating to Allah
• Seven parts of our body touch the
ground…
• Head (Forehead & nose)
• Both hands
• Both knees
• Both feet
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During Umrah
Tawaf Ka’bah: The circumfering of the
Ka'bah 7 times:
• 7 rounds of Sai’
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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)
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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).
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What to Sacrifice on Eid-ulAdha?
• 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).
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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.
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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)
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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)
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• I read an article a while back about
Cicada's(a type of insect) link with prime
numbers, pretty cool how they use prime
numbers for their survival.
• Here is the link Mathematicians explore
cicada's mysterious link with primes
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• Cicada's are insects which hibernate
underground and emerge every 13 or 17
years to mate and die (while the newborn
cicadas head underground to repeat the
process). Some people have speculated
that the 13/17-year hibernation is the
result of evolutionary pressures.
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• If cicadas hibernated for X years and had
a predator which underwent similar multiyear hibernations, say for Y years, then
the cicadas would get eaten if Y divided X.
So by "choosing" prime numbers, they
made their predators much less likely to
wake up at the right time.I guess we have
so much to learn from insects as well.
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Number 19 in Quran
• The Qur'an consists of 114 (19 x 6) Suras.
• Another mathematical miracle of the
Qur'an is the manner in which the number
19 is numerologically encoded in verses.
This number is stressed in the words of
the Qur'an: "There are nineteen (angels)
in charge of it." (Qur'an, 74:30), and is
encoded in various places in the Book.
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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 Qur'an 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.
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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 Qur'an.
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• 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.
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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.
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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.
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• Also the very fundamental concept of
prime numbers lies at the very heart of all
our online purchases and our banking
transactions.
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• They are used extensively in cryptography.
For example, there is an approx. 15 digit number
on your sim card.
It is the product of two prime numbers. Which
are both very large numbers. Each one of those
number identifies the user and other the carrier
location. So their factoring is impossible.
This way the 15 digit number ,even if shown
publicly cannot disclose any information to
hackers.
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