Monday, August 17, 2015

Sympy, Base 36, Project Euler #1

isblahprime

Sympy Introduction

Some of the useful functions available in the sympy package: primefactors(), factorint(), isprime(), factorial().

In [1]:
from sympy import *
In [2]:
primefactors(108)
Out[2]:
[2, 3]
In [3]:
factorint(108)
Out[3]:
{2: 2, 3: 3}
In [4]:
isprime(108)
Out[4]:
False

Activity 1: using the date format YYYYMMDD, which dates in the current month are prime numbers?

In [5]:
for d in range(20150801,20150832):
    print d, isprime(d)

20150801 False
20150802 False
20150803 False
20150804 False
20150805 False
20150806 False
20150807 False
20150808 False
20150809 False
20150810 False
20150811 False
20150812 False
20150813 False
20150814 False
20150815 False
20150816 False
20150817 False
20150818 False
20150819 False
20150820 False
20150821 True
20150822 False
20150823 False
20150824 False
20150825 False
20150826 False
20150827 False
20150828 False
20150829 False
20150830 False
20150831 False

Activity 2: using the date format YYYYMMDD, check if your birth date is prime. If not, find the first prime date after your birthday.

Number Bases

The int() function can be used to convert from any number base 2-36 to base 10.

In [6]:
int('1011',2)
Out[6]:
11

In base 16 (hexadecimal), the six letters A-F have a numerical value (in addition to the ten digits 0-9).

In [7]:
int('1F7',16)
Out[7]:
503

In base 36, all 26 letters of the alphabet have a numerical value (in addition to the ten digits 0-9).

In [8]:
x = int('PRIME',36)       # 'PRIME' is an even number; definitely not prime!
print x, isprime(x)

43274246 False
In [9]:
factorint(int('PRIME',36))     # prime factorization of 'PRIME'
Out[9]:
{2: 1, 21637123: 1}
In [10]:
x = int('BLAH',36)                  # 'BLAH' is prime!
print x, isprime(int('BLAH',36))   

540809 True

ProjectEuler.net -- Problem #1

If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23.

Find the sum of all the multiples of 3 or 5 below 1000.

In [11]:
a = range(3,1000,3)  # list of all natural numbers less than 1000 that are multiples of 3
b = range(5,1000,5)  # list of all natural numbers less than 1000 that are multiple of 5
c = a + b    # combine the two lists. THERE WILL BE DUPLICATES
print c,

[3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99, 102, 105, 108, 111, 114, 117, 120, 123, 126, 129, 132, 135, 138, 141, 144, 147, 150, 153, 156, 159, 162, 165, 168, 171, 174, 177, 180, 183, 186, 189, 192, 195, 198, 201, 204, 207, 210, 213, 216, 219, 222, 225, 228, 231, 234, 237, 240, 243, 246, 249, 252, 255, 258, 261, 264, 267, 270, 273, 276, 279, 282, 285, 288, 291, 294, 297, 300, 303, 306, 309, 312, 315, 318, 321, 324, 327, 330, 333, 336, 339, 342, 345, 348, 351, 354, 357, 360, 363, 366, 369, 372, 375, 378, 381, 384, 387, 390, 393, 396, 399, 402, 405, 408, 411, 414, 417, 420, 423, 426, 429, 432, 435, 438, 441, 444, 447, 450, 453, 456, 459, 462, 465, 468, 471, 474, 477, 480, 483, 486, 489, 492, 495, 498, 501, 504, 507, 510, 513, 516, 519, 522, 525, 528, 531, 534, 537, 540, 543, 546, 549, 552, 555, 558, 561, 564, 567, 570, 573, 576, 579, 582, 585, 588, 591, 594, 597, 600, 603, 606, 609, 612, 615, 618, 621, 624, 627, 630, 633, 636, 639, 642, 645, 648, 651, 654, 657, 660, 663, 666, 669, 672, 675, 678, 681, 684, 687, 690, 693, 696, 699, 702, 705, 708, 711, 714, 717, 720, 723, 726, 729, 732, 735, 738, 741, 744, 747, 750, 753, 756, 759, 762, 765, 768, 771, 774, 777, 780, 783, 786, 789, 792, 795, 798, 801, 804, 807, 810, 813, 816, 819, 822, 825, 828, 831, 834, 837, 840, 843, 846, 849, 852, 855, 858, 861, 864, 867, 870, 873, 876, 879, 882, 885, 888, 891, 894, 897, 900, 903, 906, 909, 912, 915, 918, 921, 924, 927, 930, 933, 936, 939, 942, 945, 948, 951, 954, 957, 960, 963, 966, 969, 972, 975, 978, 981, 984, 987, 990, 993, 996, 999, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 150, 155, 160, 165, 170, 175, 180, 185, 190, 195, 200, 205, 210, 215, 220, 225, 230, 235, 240, 245, 250, 255, 260, 265, 270, 275, 280, 285, 290, 295, 300, 305, 310, 315, 320, 325, 330, 335, 340, 345, 350, 355, 360, 365, 370, 375, 380, 385, 390, 395, 400, 405, 410, 415, 420, 425, 430, 435, 440, 445, 450, 455, 460, 465, 470, 475, 480, 485, 490, 495, 500, 505, 510, 515, 520, 525, 530, 535, 540, 545, 550, 555, 560, 565, 570, 575, 580, 585, 590, 595, 600, 605, 610, 615, 620, 625, 630, 635, 640, 645, 650, 655, 660, 665, 670, 675, 680, 685, 690, 695, 700, 705, 710, 715, 720, 725, 730, 735, 740, 745, 750, 755, 760, 765, 770, 775, 780, 785, 790, 795, 800, 805, 810, 815, 820, 825, 830, 835, 840, 845, 850, 855, 860, 865, 870, 875, 880, 885, 890, 895, 900, 905, 910, 915, 920, 925, 930, 935, 940, 945, 950, 955, 960, 965, 970, 975, 980, 985, 990, 995]
In [12]:
d = set(c)           # convert to a set to remove duplicates
print d,

set([3, 5, 6, 9, 10, 12, 15, 18, 20, 21, 24, 25, 27, 30, 33, 35, 36, 39, 40, 42, 45, 48, 50, 51, 54, 55, 57, 60, 63, 65, 66, 69, 70, 72, 75, 78, 80, 81, 84, 85, 87, 90, 93, 95, 96, 99, 100, 102, 105, 108, 110, 111, 114, 115, 117, 120, 123, 125, 126, 129, 130, 132, 135, 138, 140, 141, 144, 145, 147, 150, 153, 155, 156, 159, 160, 162, 165, 168, 170, 171, 174, 175, 177, 180, 183, 185, 186, 189, 190, 192, 195, 198, 200, 201, 204, 205, 207, 210, 213, 215, 216, 219, 220, 222, 225, 228, 230, 231, 234, 235, 237, 240, 243, 245, 246, 249, 250, 252, 255, 258, 260, 261, 264, 265, 267, 270, 273, 275, 276, 279, 280, 282, 285, 288, 290, 291, 294, 295, 297, 300, 303, 305, 306, 309, 310, 312, 315, 318, 320, 321, 324, 325, 327, 330, 333, 335, 336, 339, 340, 342, 345, 348, 350, 351, 354, 355, 357, 360, 363, 365, 366, 369, 370, 372, 375, 378, 380, 381, 384, 385, 387, 390, 393, 395, 396, 399, 400, 402, 405, 408, 410, 411, 414, 415, 417, 420, 423, 425, 426, 429, 430, 432, 435, 438, 440, 441, 444, 445, 447, 450, 453, 455, 456, 459, 460, 462, 465, 468, 470, 471, 474, 475, 477, 480, 483, 485, 486, 489, 490, 492, 495, 498, 500, 501, 504, 505, 507, 510, 513, 515, 516, 519, 520, 522, 525, 528, 530, 531, 534, 535, 537, 540, 543, 545, 546, 549, 550, 552, 555, 558, 560, 561, 564, 565, 567, 570, 573, 575, 576, 579, 580, 582, 585, 588, 590, 591, 594, 595, 597, 600, 603, 605, 606, 609, 610, 612, 615, 618, 620, 621, 624, 625, 627, 630, 633, 635, 636, 639, 640, 642, 645, 648, 650, 651, 654, 655, 657, 660, 663, 665, 666, 669, 670, 672, 675, 678, 680, 681, 684, 685, 687, 690, 693, 695, 696, 699, 700, 702, 705, 708, 710, 711, 714, 715, 717, 720, 723, 725, 726, 729, 730, 732, 735, 738, 740, 741, 744, 745, 747, 750, 753, 755, 756, 759, 760, 762, 765, 768, 770, 771, 774, 775, 777, 780, 783, 785, 786, 789, 790, 792, 795, 798, 800, 801, 804, 805, 807, 810, 813, 815, 816, 819, 820, 822, 825, 828, 830, 831, 834, 835, 837, 840, 843, 845, 846, 849, 850, 852, 855, 858, 860, 861, 864, 865, 867, 870, 873, 875, 876, 879, 880, 882, 885, 888, 890, 891, 894, 895, 897, 900, 903, 905, 906, 909, 910, 912, 915, 918, 920, 921, 924, 925, 927, 930, 933, 935, 936, 939, 940, 942, 945, 948, 950, 951, 954, 955, 957, 960, 963, 965, 966, 969, 970, 972, 975, 978, 980, 981, 984, 985, 987, 990, 993, 995, 996, 999])
In [13]:
sum(d)  # the solution to problem 1
Out[13]:
233168

Resources

Posted by at
Subscribe to: Comments (Atom)