Edmund Landau (1877-1938 ) was a number theorist who published a proof of the Prime Number Theorem that was simpler than those of Hadamard and de la Vallée Poussin. In 1912, he gave an address to the Fifth International Congress of Mathematicians at Cambridge, England. He described four intractable problems: (1) Goldbach Conjecture, (2) the twin primes conjecture, (3) infinite primes of n²+1, and (4) a prime between n² and (n+1)². Apparently, what he had in mind is a table of numbers similar to the multiplication table of elementary arithmetic where the perfect squares are found arranged in ascending or descending order along the diagonal.

However, within the sieve of Diophantus the odd perfect squares: 9, 25, 49, 81, 121, 169, etc. are found more in the lower left half than ones found in the upper right half and the elements along the diagonal are now replaced by multiples of 5 which necessarily includes perfect squares of these multiples: 5²=25, 10²=100, 15²=225, 20²=400, 25²=625, 30²=900, 35²=1225, etc. but n²+1 is a prime if and only if n² does not occupy either of the two prime positions at relative group indices G22 and G32 and n²+1 either fills G22 or G32. Therefore, places of perfect squares of odd numbers are all allowed to occupy the two prime positions at G22 and G32, when they do they are considered as missing primes.