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Prime Numbers Lecture L4.4 Sieve of Eratosthenes
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// first create an array of flags, where // each member of the array stands for a odd number // starting with 3. for (j = 0; j < size; j++) { flags[j] = 1; } Find prime numbers using Sieve of Eratosthenes j 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 size = 1024
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Find prime numbers using Sieve of Eratosthenes j 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 primeCount = 0; for (j = 0; j < size; j++) { if (flags[j] == 1) { // found a prime, count it primeCount++; // now set all of the multiples of // the current prime number to false // because they couldn't possibly be prime a = 2*j + 3;// odd numbers starting with 3 b = a + j; while(b < size) { flags[b] = 0; b = b + a; } a b 3 3 5 6 7 9 9 12 1115 13 18 15 21 17 24 19 27 21 30 23 33 25 36 27 39 29 42 31 45 33 48
![Find prime numbers using Sieve of Eratosthenes j primeCount = 0; for (j = 0; j < size; j++) { if (flags[j] == 1) { // found a prime, count it primeCount++; // now set all of the multiples of // the current prime number to false // because they couldn t possibly be prime a = 2*j + 3;// odd numbers starting with 3 b = a + j; while(b < size) { flags[b] = 0; b = b + a; } a b](http://images.slideplayer.com/34/10256120/slides/slide_3.jpg "Find prime numbers using Sieve of Eratosthenes j primeCount = 0; for (j = 0; j < size; j++) { if (flags[j] == 1) { // found a prime, count it primeCount++; // now set all of the multiples of // the current prime number to false // because they couldn t possibly be prime a = 2*j + 3;// odd numbers starting with 3 b = a + j; while(b < size) { flags[b] = 0; b = b + a; } a b")
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Find prime numbers using Sieve of Eratosthenes j 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 primeCount = 0; for (j = 0; j < size; j++) { if (flags[j] == 1) { // found a prime, count it primeCount++; // now set all of the multiples of // the current prime number to false // because they couldn't possibly be prime a = 2*j + 3;// odd numbers starting with 3 b = a + j; while(b < size) { flags[b] = 0; b = b + a; } a b 3 3 5 6 7 9 9 12 1115 13 18 15 21 17 24 19 27 21 30 23 33 25 36 27 39 29 42 31 45 33 48
![Find prime numbers using Sieve of Eratosthenes j primeCount = 0; for (j = 0; j < size; j++) { if (flags[j] == 1) { // found a prime, count it primeCount++; // now set all of the multiples of // the current prime number to false // because they couldn t possibly be prime a = 2*j + 3;// odd numbers starting with 3 b = a + j; while(b < size) { flags[b] = 0; b = b + a; } a b](http://images.slideplayer.com/34/10256120/slides/slide_4.jpg "Find prime numbers using Sieve of Eratosthenes j primeCount = 0; for (j = 0; j < size; j++) { if (flags[j] == 1) { // found a prime, count it primeCount++; // now set all of the multiples of // the current prime number to false // because they couldn t possibly be prime a = 2*j + 3;// odd numbers starting with 3 b = a + j; while(b < size) { flags[b] = 0; b = b + a; } a b")
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Find prime numbers using Sieve of Eratosthenes j 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 primeCount = 0; for (j = 0; j < size; j++) { if (flags[j] == 1) { // found a prime, count it primeCount++; // now set all of the multiples of // the current prime number to false // because they couldn't possibly be prime a = 2*j + 3;// odd numbers starting with 3 b = a + j; while(b < size) { flags[b] = 0; b = b + a; } a b 3 3 5 6 7 9 9 12 1115 13 18 15 21 17 24 19 27 21 30 23 33 25 36 27 39 29 42 31 45 33 48
![Find prime numbers using Sieve of Eratosthenes j primeCount = 0; for (j = 0; j < size; j++) { if (flags[j] == 1) { // found a prime, count it primeCount++; // now set all of the multiples of // the current prime number to false // because they couldn t possibly be prime a = 2*j + 3;// odd numbers starting with 3 b = a + j; while(b < size) { flags[b] = 0; b = b + a; } a b](http://images.slideplayer.com/34/10256120/slides/slide_5.jpg "Find prime numbers using Sieve of Eratosthenes j primeCount = 0; for (j = 0; j < size; j++) { if (flags[j] == 1) { // found a prime, count it primeCount++; // now set all of the multiples of // the current prime number to false // because they couldn t possibly be prime a = 2*j + 3;// odd numbers starting with 3 b = a + j; while(b < size) { flags[b] = 0; b = b + a; } a b")
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Find prime numbers using Sieve of Eratosthenes j 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 1 1 0 1 1 0 1 1 0 1 1 1 1 1 1 primeCount = 0; for (j = 0; j < size; j++) { if (flags[j] == 1) { // found a prime, count it primeCount++; // now set all of the multiples of // the current prime number to false // because they couldn't possibly be prime a = 2*j + 3;// odd numbers starting with 3 b = a + j; while(b < size) { flags[b] = 0; b = b + a; } a b 3 3 5 6 7 9 9 12 1115 13 18 15 21 17 24 19 27 21 30 23 33 25 36 27 39 29 42 31 45 33 48
![Find prime numbers using Sieve of Eratosthenes j primeCount = 0; for (j = 0; j < size; j++) { if (flags[j] == 1) { // found a prime, count it primeCount++; // now set all of the multiples of // the current prime number to false // because they couldn t possibly be prime a = 2*j + 3;// odd numbers starting with 3 b = a + j; while(b < size) { flags[b] = 0; b = b + a; } a b](http://images.slideplayer.com/34/10256120/slides/slide_6.jpg "Find prime numbers using Sieve of Eratosthenes j primeCount = 0; for (j = 0; j < size; j++) { if (flags[j] == 1) { // found a prime, count it primeCount++; // now set all of the multiples of // the current prime number to false // because they couldn t possibly be prime a = 2*j + 3;// odd numbers starting with 3 b = a + j; while(b < size) { flags[b] = 0; b = b + a; } a b")
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Find prime numbers using Sieve of Eratosthenes j 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 1 1 0 1 1 0 1 1 0 1 1 0 1 1 1 primeCount = 0; for (j = 0; j < size; j++) { if (flags[j] == 1) { // found a prime, count it primeCount++; // now set all of the multiples of // the current prime number to false // because they couldn't possibly be prime a = 2*j + 3;// odd numbers starting with 3 b = a + j; while(b < size) { flags[b] = 0; b = b + a; } a b 3 3 5 6 7 9 9 12 1115 13 18 15 21 17 24 19 27 21 30 23 33 25 36 27 39 29 42 31 45 33 48
![Find prime numbers using Sieve of Eratosthenes j primeCount = 0; for (j = 0; j < size; j++) { if (flags[j] == 1) { // found a prime, count it primeCount++; // now set all of the multiples of // the current prime number to false // because they couldn t possibly be prime a = 2*j + 3;// odd numbers starting with 3 b = a + j; while(b < size) { flags[b] = 0; b = b + a; } a b](http://images.slideplayer.com/34/10256120/slides/slide_7.jpg "Find prime numbers using Sieve of Eratosthenes j primeCount = 0; for (j = 0; j < size; j++) { if (flags[j] == 1) { // found a prime, count it primeCount++; // now set all of the multiples of // the current prime number to false // because they couldn t possibly be prime a = 2*j + 3;// odd numbers starting with 3 b = a + j; while(b < size) { flags[b] = 0; b = b + a; } a b")
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Find prime numbers using Sieve of Eratosthenes j 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 primeCount = 0; for (j = 0; j < size; j++) { if (flags[j] == 1) { // found a prime, count it primeCount++; // now set all of the multiples of // the current prime number to false // because they couldn't possibly be prime a = 2*j + 3;// odd numbers starting with 3 b = a + j; while(b < size) { flags[b] = 0; b = b + a; } a b 3 3 5 6 7 9 9 12 1115 13 18 15 21 17 24 19 27 21 30 23 33 25 36 27 39 29 42 31 45 33 48
![Find prime numbers using Sieve of Eratosthenes j primeCount = 0; for (j = 0; j < size; j++) { if (flags[j] == 1) { // found a prime, count it primeCount++; // now set all of the multiples of // the current prime number to false // because they couldn t possibly be prime a = 2*j + 3;// odd numbers starting with 3 b = a + j; while(b < size) { flags[b] = 0; b = b + a; } a b](http://images.slideplayer.com/34/10256120/slides/slide_8.jpg "Find prime numbers using Sieve of Eratosthenes j primeCount = 0; for (j = 0; j < size; j++) { if (flags[j] == 1) { // found a prime, count it primeCount++; // now set all of the multiples of // the current prime number to false // because they couldn t possibly be prime a = 2*j + 3;// odd numbers starting with 3 b = a + j; while(b < size) { flags[b] = 0; b = b + a; } a b")
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Find prime numbers using Sieve of Eratosthenes j 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 1 1 0 1 1 0 1 1 0 1 0 0 1 1 0 primeCount = 0; for (j = 0; j < size; j++) { if (flags[j] == 1) { // found a prime, count it primeCount++; // now set all of the multiples of // the current prime number to false // because they couldn't possibly be prime a = 2*j + 3;// odd numbers starting with 3 b = a + j; while(b < size) { flags[b] = 0; b = b + a; } a b 3 3 5 6 7 9 9 12 1115 13 18 15 21 17 24 19 27 21 30 23 33 25 36 27 39 29 42 31 45 33 48
![Find prime numbers using Sieve of Eratosthenes j primeCount = 0; for (j = 0; j < size; j++) { if (flags[j] == 1) { // found a prime, count it primeCount++; // now set all of the multiples of // the current prime number to false // because they couldn t possibly be prime a = 2*j + 3;// odd numbers starting with 3 b = a + j; while(b < size) { flags[b] = 0; b = b + a; } a b](http://images.slideplayer.com/34/10256120/slides/slide_9.jpg "Find prime numbers using Sieve of Eratosthenes j primeCount = 0; for (j = 0; j < size; j++) { if (flags[j] == 1) { // found a prime, count it primeCount++; // now set all of the multiples of // the current prime number to false // because they couldn t possibly be prime a = 2*j + 3;// odd numbers starting with 3 b = a + j; while(b < size) { flags[b] = 0; b = b + a; } a b")
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