The RSA cryptosystem, invented by Ron Rivest, Adi Shamir and Len Adleman was first publicized in the August 1977 issue of Scientific American. The security level of this algorithm very much depends on two large prime numbers. To check the primality of large number in personal computer is huge time consuming using the best known trial division algorithm. The time complexity for primality testing has been reduced using the representation of divisors in the form of 6n±1. According to the fundamental theorem of Arithmetic, every number has unique factorization. So to check primality, it is sufficient to check if the number is divisible by any prime below the square root of the number. The set of divisors obtained by 6n±1 form representation contains many composites. These composite numbers have been reduced by 30k approach. In this paper, the number of composites has been further reduced using 210k approach. A performance analysis in time complexity has been given between 210k approach and other prior applied methods. It has been observed that the time complexity for primality testing has been reduced using 210k approach.

A human eye can detect a face in an image whether it is in a digital image or also in some video. The same thing is highly challenging for a machine. There are lots of algorithms available to detect human face. In this paper, a technique has been made to detect and locate the position of human faces in digital images. This approach has two steps. First, training the artificial neural network using Levenberg–Marquardt training algorithm and then the proposed algorithm has been used to detect and locate the position of the human faces from digital image. The proposed algorithm has been implemented for six color spaces which are RGB, YES, YUV, YCbCr, YIQ and CMY for each of the image formats bmp, jpeg, gif, tiff and png. For each color space training has been made for the image formats bmp, jpeg, gif, tiff and png. Finally, one color space and particular image format has been selected for face detection and location in digital image based on the performance and accuracy.