Secret image sharing is a technique for protecting secret information that is fault-tolerant by splitting a secret image into multiple shadow images. In this paper, we address the lack of research on current colour secret image sharing schemes and propose a new scheme in combination with the theory of prime number distribution. The scheme deals directly with the three components of each pixel value of the secret image. The three components of the pixel value are first mapped to the sequence number of the approximate pixel set in which they are located, then a specific function is selected to perform the mapping operation on the RGB intensity values using mathematical transformations, and finally a k − 1 polynomial is used to generate the shared shares. When reconstructing, a value from the approximate pixel set where the pixel value is located will be selected randomly as the restored value.Unlike most image visual share schemes, this algorithm does not require the use of random permutations to convert a secret image into a random image, thus making the scheme simpler and more reliable. In addition, the shared images generated by this scheme are smaller in size than the secret images. Finally, the secret image can be recovered through the set of eligible participants.