3 and 5 are “twin primes”: They’re two prime numbers that differ by 2. Further such pairs are 5 and 7, and 11 and 13. These pairs get sparser as you travel out the number line, but no one knows whether they eventually cease appearing altogether.

University of Alberta mathematician Leo Moser saw an opportunity in this pattern — if a prime magic square can be fashioned from the smaller partners in these pairs:

  29 1061  179  227

 269  137 1019   71

1049  101  239  107

149   197   59 1091

… then it immediately suggests a second prime square produced from the larger:

  31 1063  181  229

 271  139 1021   73

1051  103  241  109

 151  199   61 1093

(“Strictly for Squares,” Recreational Mathematics Magazine 1:5 [October 1961].)