How to display a sequence of numbers in column-major order?

Question

Program description: Find all the prime numbers between 1 and 4,027 and print them in a table which "reads down", using as few rows as possible, and using as few sheets of paper as possible. (This is because I have to print them out on paper to turn it in.) All numbers should be right-justified in their column. The height of the columns should all be the same, except for perhaps the last column, which might have a few blank entries towards its bottom row.

The plan for my first function is to find all prime numbers between the range above and put them in a list. Then I want my second function to display the list in a table that reads up to down.

2    23    59
3    29    61
5    31    67
7    37    71
11   41    73
13   43    79
17   47    83
19   53    89

ect...

This all I've been able to come up with myself:

def findPrimes(n):
    """ Adds calculated prime numbers to a list. """
    prime_list = list()
    for number in range(1, n + 1):
        prime = True
        for i in range(2, number):
            if(number % i == 0):
                prime = False
        if prime:
            prime_list.append(number)

    return prime_list

def displayPrimes():
    pass

print(findPrimes(4027))

I'm not sure how to make a row/column display in Python. I remember using Java in my previous class and we had to use a for loop inside a for loop I believe. Do I have to do something similar to that?

Answer 1

Although I frequently don't answer questions where the original poster hasn't even made an attempt to solve the problem themselves, I decided to make an exception of yours—mostly because I found it an interesting (and surprisingly challenging) problem that required solving a number of somewhat tricky sub-problems.

I also optimized your find_primes() function slightly by taking advantage of some reatively well-know computational shortcuts for calculating them.

For testing and demo purposes, I made the tables only 15 rows high to force more than one page to be generated as shown in the output at the end.

from itertools import zip_longest
import locale
import math
locale.setlocale(locale.LC_ALL, '')  # enable locale-specific formatting

def zip_discard(*iterables, _NULL=object()):
    """ Like zip_longest() but doesn't fill out all rows to equal length.
     https://stackoverflow.com/questions/38054593/zip-longest-without-fillvalue
    """
    return [[entry for entry in iterable if entry is not _NULL]
                for iterable in zip_longest(*iterables, fillvalue=_NULL)]

def grouper(n, seq):
    """ Group elements in sequence into groups of "n" items. """
    for i in range(0, len(seq), n):
        yield seq[i:i+n]

def tabularize(width, height, numbers):
    """ Print list of numbers in column-major tabular form given the dimensions
        of the table in characters (rows and columns). Will create multiple
        tables of required to display all numbers.
    """
    # Determine number of chars needed to hold longest formatted numeric value
    gap = 2  # including space between numbers
    col_width = len('{:n}'.format(max(numbers))) + gap

    # Determine number of columns that will fit within the table's width.
    num_cols = width // col_width
    chunk_size = num_cols * height  # maximum numbers in each table

    for i, chunk in enumerate(grouper(chunk_size, numbers), start=1):
        print('---- Page {} ----'.format(i))
        num_rows = int(math.ceil(len(chunk) / num_cols))  # rounded up
        table = zip_discard(*grouper(num_rows, chunk))
        for row in table:
            print(''.join(('{:{width}n}'.format(num, width=col_width)
                                                    for num in row)))

def find_primes(n):
    """ Create list of prime numbers from 1 to n. """
    prime_list = []
    for number in range(1, n+1):
        for i in range(2, int(math.sqrt(number)) + 1):
            if not number % i:  # Evenly divisible?
                break  # Not prime.
        else:
            prime_list.append(number)

    return prime_list

primes = find_primes(4027)
tabularize(80, 15, primes)

Output:

---- Page 1 ----
      1     47    113    197    281    379    463    571    659    761    863
      2     53    127    199    283    383    467    577    661    769    877
      3     59    131    211    293    389    479    587    673    773    881
      5     61    137    223    307    397    487    593    677    787    883
      7     67    139    227    311    401    491    599    683    797    887
     11     71    149    229    313    409    499    601    691    809    907
     13     73    151    233    317    419    503    607    701    811    911
     17     79    157    239    331    421    509    613    709    821    919
     19     83    163    241    337    431    521    617    719    823    929
     23     89    167    251    347    433    523    619    727    827    937
     29     97    173    257    349    439    541    631    733    829    941
     31    101    179    263    353    443    547    641    739    839    947
     37    103    181    269    359    449    557    643    743    853    953
     41    107    191    271    367    457    563    647    751    857    967
     43    109    193    277    373    461    569    653    757    859    971
---- Page 2 ----
    977  1,069  1,187  1,291  1,427  1,511  1,613  1,733  1,867  1,987  2,087
    983  1,087  1,193  1,297  1,429  1,523  1,619  1,741  1,871  1,993  2,089
    991  1,091  1,201  1,301  1,433  1,531  1,621  1,747  1,873  1,997  2,099
    997  1,093  1,213  1,303  1,439  1,543  1,627  1,753  1,877  1,999  2,111
  1,009  1,097  1,217  1,307  1,447  1,549  1,637  1,759  1,879  2,003  2,113
  1,013  1,103  1,223  1,319  1,451  1,553  1,657  1,777  1,889  2,011  2,129
  1,019  1,109  1,229  1,321  1,453  1,559  1,663  1,783  1,901  2,017  2,131
  1,021  1,117  1,231  1,327  1,459  1,567  1,667  1,787  1,907  2,027  2,137
  1,031  1,123  1,237  1,361  1,471  1,571  1,669  1,789  1,913  2,029  2,141
  1,033  1,129  1,249  1,367  1,481  1,579  1,693  1,801  1,931  2,039  2,143
  1,039  1,151  1,259  1,373  1,483  1,583  1,697  1,811  1,933  2,053  2,153
  1,049  1,153  1,277  1,381  1,487  1,597  1,699  1,823  1,949  2,063  2,161
  1,051  1,163  1,279  1,399  1,489  1,601  1,709  1,831  1,951  2,069  2,179
  1,061  1,171  1,283  1,409  1,493  1,607  1,721  1,847  1,973  2,081  2,203
  1,063  1,181  1,289  1,423  1,499  1,609  1,723  1,861  1,979  2,083  2,207
---- Page 3 ----
  2,213  2,333  2,423  2,557  2,687  2,789  2,903  3,037  3,181  3,307  3,413
  2,221  2,339  2,437  2,579  2,689  2,791  2,909  3,041  3,187  3,313  3,433
  2,237  2,341  2,441  2,591  2,693  2,797  2,917  3,049  3,191  3,319  3,449
  2,239  2,347  2,447  2,593  2,699  2,801  2,927  3,061  3,203  3,323  3,457
  2,243  2,351  2,459  2,609  2,707  2,803  2,939  3,067  3,209  3,329  3,461
  2,251  2,357  2,467  2,617  2,711  2,819  2,953  3,079  3,217  3,331  3,463
  2,267  2,371  2,473  2,621  2,713  2,833  2,957  3,083  3,221  3,343  3,467
  2,269  2,377  2,477  2,633  2,719  2,837  2,963  3,089  3,229  3,347  3,469
  2,273  2,381  2,503  2,647  2,729  2,843  2,969  3,109  3,251  3,359  3,491
  2,281  2,383  2,521  2,657  2,731  2,851  2,971  3,119  3,253  3,361  3,499
  2,287  2,389  2,531  2,659  2,741  2,857  2,999  3,121  3,257  3,371  3,511
  2,293  2,393  2,539  2,663  2,749  2,861  3,001  3,137  3,259  3,373  3,517
  2,297  2,399  2,543  2,671  2,753  2,879  3,011  3,163  3,271  3,389  3,527
  2,309  2,411  2,549  2,677  2,767  2,887  3,019  3,167  3,299  3,391  3,529
  2,311  2,417  2,551  2,683  2,777  2,897  3,023  3,169  3,301  3,407  3,533
---- Page 4 ----
  3,539  3,581  3,623  3,673  3,719  3,769  3,823  3,877  3,919  3,967  4,019
  3,541  3,583  3,631  3,677  3,727  3,779  3,833  3,881  3,923  3,989  4,021
  3,547  3,593  3,637  3,691  3,733  3,793  3,847  3,889  3,929  4,001  4,027
  3,557  3,607  3,643  3,697  3,739  3,797  3,851  3,907  3,931  4,003
  3,559  3,613  3,659  3,701  3,761  3,803  3,853  3,911  3,943  4,007
  3,571  3,617  3,671  3,709  3,767  3,821  3,863  3,917  3,947  4,013