文摘
We show that there are infinitely many distinct rational primes of the form p1=a2+b2 and p2=a2+(b+h)2, with ca9fccf046f48e5445" title="Click to view the MathML source">a,b,h integers, such that aebe8" title="Click to view the MathML source">|h|≤246. We do this by viewing a Gaussian prime c+di as a lattice point ca099" title="Click to view the MathML source">(c,d) in R2 and showing that there are infinitely many pairs of distinct Gaussian primes (c1,d1) and (c2,d2) such that the Euclidean distance between them is bounded by 246. Our method, motivated by the work of Maynard [9] and the Polymath project [13], is applicable to the wider setting of imaginary quadratic fields with class number 1 and yields better results than those previously obtained for gaps between primes in the corresponding number rings.