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Anxiety, learning disabilities, and depression are the symptoms of attention deficit hyperactivity disorder (ADHD), an isogenous pattern of hyperactivity, impulsivity, and inattention. For the early diagnosis of ADHD, electroencephalogram (EEG) signals are widely used. However, the direct analysis of an EEG is highly challenging as it is time-consuming, nonlinear, and nonstationary in nature. Thus, in this paper, a novel approach (LSGP-USFNet) is developed based on the patterns obtained from Ulam’s spiral and Sophia Germain’s prime numbers. The EEG signals are initially filtered to remove the noise and segmented with a non-overlapping sliding window of a length of 512 samples. Then, a time–frequency analysis approach, namely continuous wavelet transform, is applied to each channel of the segmented EEG signal to interpret it in the time and frequency domain. The obtained time–frequency representation is saved as a time–frequency image, and a non-overlapping n × n sliding window is applied to this image for patch extraction. An n × n Ulam’s spiral is localized on each patch, and the gray levels are acquired from this patch as features where Sophie Germain’s primes are located in Ulam’s spiral. All gray tones from all patches are concatenated to construct the features for ADHD and normal classes. A gray tone selection algorithm, namely ReliefF, is employed on the representative features to acquire the final most important gray tones. The support vector machine classifier is used with a 10-fold cross-validation criteria. Our proposed approach, LSGP-USFNet, was developed using a publicly available dataset and obtained an accuracy of 97.46% in detecting ADHD automatically. Our generated model is ready to be validated using a bigger database and it can also be used to detect other children’s neurological disorders.