Yes it can.

Ulam's Spiral, (sometimes known as "Ulam's Cloth"), is a graphical representation of the natural positive integers which exhibits some remarkable patterns amongst the prime numbers. It was discovered by the nuclear physicist Stanislav Ulam in 1963. It has been the subject of large amounts of investigation and speculation ever since. Ulam's observation was so striking that it featured on the cover of the March 1964 edition of Scientific American.

See the following link for further information and links relating to Ulam's Spiral: http://en.wikipedia.org/wiki/Ulam_spiral

Ulam's Spiral comprises a square pattern where the length of each side increases by 2, (from an initial length of 3), with each rotation of the spiral. The lowest number in each ring is offset, from the first vertex in each ring, by one space in the direction of rotation. This ensures that the highest number in each ring appears adjacent to the lowest number in the next ring, giving the appearance of a spiral about the central number. The spiral is traditionally drawn anti-clockwise with number 1 in the centre and number 2 appearing at the 3 O'Clock position.

The prominent diagonal lines which appear in Ulam's Spiral are generally explained by reference to quadratic formulae which, when applied to small positive integers, produce large numbers of primes.

For example, Euler's Formula:

      4x² - 2x + 41

produces prime numbers for the 40 consecutive integers x = 0 to 39.

The following picture, a montage of 8 separate Apophenia plots, shows various quadratic formulae applied to the ring index number, r. All prime numbers generated by the formulae are coloured according to the key. Note that not all of the primes so generated appear on the NW-SE or NE-SW diagonal lines; many appear on lines which spiral around the centre before joining the diagonals:

Using Apophenia nomenclature, the traditional layout of Ulam's Spiral corresponds to the following program settings:

      (-) P4 I3 G2 R-1 A45

L and H can be set to any desired numbers in the range H>L>0. The plotted pattern is particularly striking when L is set to 41 since 40 prime numbers appear side-by-side in a diagonal line either side of the centre point:

 

Apophenia allows the user to investigate many novel prime number patterns in polygons of all orders by adopting a simple concentric polygon approach to the display of the natural numbers, not necessarily involving spirals.