Sophie Germain-Portrait aus Primzahl-Pixeln

gauss

Superclevere Arbeit aus der Mathe-Kunst-Ausstellung der 2016er Bridge Konferenz: Zachary Abel hat eine Primzahl gefunden, deren 5671 Ziffern in einem Grid von 53x107 Pixeln, deren Helligkeit nach dem Wert der jeweiligen Stelle (von 1=dunkel nach 9=hell) vergeben wird, ein Portrait der Mathematikern Sophie Germain ergibt. Und um das ganze noch zu überclevern, die Primzahl ist eine Sophie-Germain-Primzahl. Das is' so clever, das geht eigentlich gar nicht.

In this piece, a prime number P was carefully chosen so that its 53x107=5671 digits, when arranged in a grid (in order) and shaded by value, reveal a portrait of Sophie Germain. In fact, this prime P was even more carefully chosen so that 2P+1 is also prime, thus making P a Sophie Germain prime in the mathematical sense (like 53, since 2x53+1=107 is also prime). The existence of a Sophie Germain prime bearing Sophie Germain's appearance highlights the conjectured high density of Sophie Germain primes: even though they are rarer than regular primes, they are believed to possess a similar ubiquity.

Und weil Zachary so'n Cleverle ist, hat er mit demselben Prinzip dann ein Gauss-Portrait aus zwei Gauß-Primzahlen gebastelt. Smartass.

In "Gaussian Gaussian Prime", two integers A and B are drawn in separate 145x72 grids (A is drawn in red on the left, and B is drawn in blue on the right), where A and B are chosen so that the Gaussian integer A+Bi cannot be (nontrivially) factored into smaller Gaussian integers, i.e., A+Bi is mathematically a Gaussian Prime. These are known to possess density properties in the complex plane that are similar to those of integer primes on the real line.