Python code to generate and print Ulam Spirals.
A Python module to create Ulam Spirals. An Ulam spiral is a regular rectangular grid of integers, starting at 1 (or, optionally, some other positive integer or zero) at the center and spiraling outwardly.
This code implements Ulam Spirals spiraling clockwise.
The module implements a class which is initiated with an end integer (and an optional start integer).
>>> import ulamspiral
>>> S = ulamspiral.UlamSpiral(24)
>>> S.show()
21 22 23 24
20 7 8 9 10
19 6 1 2 11
18 5 4 3 12
17 16 15 14 13
>>> S = ulamspiral.UlamSpiral(24, start=0)
>>> S.show()
20 21 22 23 24
19 6 7 8 9
18 5 0 1 10
17 4 3 2 11
16 15 14 13 12
>>> ulamspiral.UlamSpiral(200, start=0).show()
156 157 158 159 160 161 162 163 164 165 166 167 168 169
155 110 111 112 113 114 115 116 117 118 119 120 121 170
154 109 72 73 74 75 76 77 78 79 80 81 122 171
153 108 71 42 43 44 45 46 47 48 49 82 123 172
152 107 70 41 20 21 22 23 24 25 50 83 124 173
151 106 69 40 19 6 7 8 9 26 51 84 125 174
150 105 68 39 18 5 0 1 10 27 52 85 126 175
149 104 67 38 17 4 3 2 11 28 53 86 127 176
148 103 66 37 16 15 14 13 12 29 54 87 128 177
200 147 102 65 36 35 34 33 32 31 30 55 88 129 178
199 146 101 64 63 62 61 60 59 58 57 56 89 130 179
198 145 100 99 98 97 96 95 94 93 92 91 90 131 180
197 144 143 142 141 140 139 138 137 136 135 134 133 132 181
196 195 194 193 192 191 190 189 188 187 186 185 184 183 182Clone this repository (minimally, all that is needed is the ulamspiral.py file) and place the
ulamspiral.py file in your Python's path. (There is no setup script currently.)
The interest in this rectangular spiral of integers comes from the fact that primes are arranged in diagonal lines with a probability higher than one might expect. We can view this phenomenon as follows.
We write the following script, which generates primes with a sieve and then displays only prime integers in an Ulam spiral.
#!/usr/bin/python2
import ulamspiral
limit = 700
def primes_range(stop):
""" Form a prime sieve and return a list of primes below 'stop'."""
primes = [True] * stop
primes[0], primes[1] = [False] * 2
L = []
for ind, val in enumerate(primes):
if val:
primes[ind*2::ind] = [False] * (((stop - 1)//ind) - 1)
L.append(ind)
return L
# Form the Ulam Spiral
S = ulamspiral.UlamSpiral(limit)
# Form the list of primes
P = set(primes_range(limit))
# Show only primes in the spiral
# Determine character width for printing
char_width = len(str(max([max(i) for i in S.rows]))) + 1
for row in S.rows:
row_str = ''
for i in row:
if i <= S.max_int and i in P:
row_str += str(i).rjust(char_width)
else:
row_str += ''.rjust(char_width)
print row_str$ python diagonal_primes.py
601 607 613 617 619
509 521 523
599 421 431 433 439
347 349 353 359 443
419 277 281 283
503 211 223 631
271 157 163 167 227
113 293
593 269 73 79 229 367
499 337 109 43 47 83 173 449
71 23
691 107 41 7
151 19 2 11 53 127 233 541
5 3 29
587 409 263 149 67 17 13 373
331 103 37 31 89 179 641
61 59 131
491 199 101 97 181 457 643
139 137 239 547
683 197 193 191
257 251 241 379
487 317 313 311 307 461 647
401 397 389 383
479 467 463
577 571 569 563 557
677 673 661 659 653