In some embodiments, an apparatus includes logical interrupt identification number creation logic to receive physical processor identification numbers and create logical processor identification numbers through using the physical processor identification numbers. Each of the logical processor identification numbers corresponds to one of the physical processor identification numbers, and the logical processor identification numbers each include a processor cluster identification number and an intra-cluster identification number. The processor cluster identification numbers are each formed to include a group of bits from the corresponding physical processor identification number shifted in position, and the intra-cluster identification numbers are each formed in response to values of others of the bits of the corresponding physical processor identification number. Other embodiments are described.