The algorithm of proven and young (APY) can be used to predict genomic (G)EBV with a single-step genomic BLUP when the number of genotyped animals is large. Since the APY approach uses an approximation of the inverse of the genomic relationship matrix, GEBV could change when different genotyped animals are chosen as core animals. The objective of this study was to investigate what creates substantial changes in GEBV with APY when different core animals are used. Two data sets were simulated: 1) 60K genotyped animals, 70K phenotypes, 100K animals in pedigree and 2) 120K genotyped animals, 140K phenotypes, 200K animals in pedigree. In both cases, phenotypes in 12 generations and genotypes in the last 6 generations were simulated, assuming the heritability 0.5 and the additive genetic standard deviation (SD(a)) 7.1. Changes in GEBV using different core animals were compared. In addition, for udder depth (1 of 18 linear type traits), 570K genotyped animals in addition to 9M phenotypes and 10M animals in pedigree were used to investigate changes in GEBV by different core animals. Maximum Difference was selected as a potential measure of model performance among individual elite animals. Unintentionally excluding close family members from the core animals needs to be taken into consideration. In the simulation study, GEBV changed the most when the status of genotyped animals moved between core and non-core when using the smallest core size (10K in this simulation). Maximum differences in GEBV were smaller for 60K genotyped animals than those for 120K genotyped animals. Reliabilities (squared correlations between GEBV and true breeding values) were similar in any core sizes but lower than that for GEBV calculated without APY. The results from udder depth were in agreement with those from simulation, and GEBV changes decreased from 73% to 16% of SD(a) for non-core genotyped animals by increasing the core size from 10K to 60K. The extremely large change in GEBV was not found. Reliabilities were similar for any core size. For simulation and udder depth, GEBV changes asymptotically decreased by increasing the core size.