Intra prediction algorithm in the recently developed high efficiency video coding (HEVC) standard has very high computational complexity. Therefore, in this paper, we propose pixel equality and pixel similarity based techniques for reducing amount of computations performed by HEVC intra prediction algorithm and, therefore, reducing energy consumption of HEVC intra prediction hardware. The proposed techniques significantly reduce the amount of computations performed by 4 x 4 and 8 x 8 luminance angular prediction modes with a small comparison overhead. Pixel equality based technique does not affect the PSNR and bit rate. Pixel similarity based technique increases the PSNR slightly for some video frames and it decreases the PSNR slightly for some video frames. We also designed and implemented a low energy HEVC intra prediction hardware for 4 x 4 and 8 x 8 angular prediction modes including the proposed techniques using Verilog HDL. The proposed techniques significantly reduce the energy consumption of this HEVC intra prediction hardware.