To reduce the risks associated with ionizing radiation, a reduction of radiation exposure in PET imaging is needed. However, this leads to a detrimental effect on image contrast and quantification. High-quality PET images synthesized from low-dose data offer a solution to reduce radiation exposure. We introduce a diffusion-model-based approach for estimating full-dose PET images from low-dose ones: the PET Consistency Model (PET-CM) yielding synthetic quality comparable to state-of-the-art diffusion-based synthesis models, but with greater efficiency. There are two steps: a forward process that adds Gaussian noise to a full dose PET image at multiple timesteps, and a reverse diffusion process that employs a PET Shifted-window Vision Transformer (PET-VIT) network to learn the denoising procedure conditioned on the corresponding low-dose PETs. In PET-CM, the reverse process learns a consistency function for direct denoising of Gaussian noise to a clean full-dose PET. We evaluated the PET-CM in generating full-dose images using only 1/8 and 1/4 of the standard PET dose. Comparing 1/8 dose to full-dose images, PET-CM demonstrated impressive performance with normalized mean absolute error (NMAE) of 1.233+/-0.131%, peak signal-to-noise ratio (PSNR) of 33.915+/-0.933dB, structural similarity index (SSIM) of 0.964+/-0.009, and normalized cross-correlation (NCC) of 0.968+/-0.011, with an average generation time of 62 seconds per patient. This is a significant improvement compared to the state-of-the-art diffusion-based model with PET-CM reaching this result 12x faster. In the 1/4 dose to full-dose image experiments, PET-CM is also competitive, achieving an NMAE 1.058+/-0.092%, PSNR of 35.548+/-0.805dB, SSIM of 0.978+/-0.005, and NCC 0.981+/-0.007 The results indicate promising low-dose PET image quality improvements for clinical applications.