The Amyloid-beta protein is related to Alzheimer's disease, and various experiments have shown that oligomers as small as the dinner are cytotoxic. Two alloforms are mainly produced: A beta(1-40) and A beta(1-42). They have very different oligomer distributions, and it was recently suggested, from experimental studies, that this variation may originate from structural differences in their dimer structures. Little structural information is available on the A beta dimer, however, and to complement experimental observations, we simulated the folding of the wild-type A beta(1-40) and A beta(1-42) dimers as well as the mutated A beta(1-40)(D23N) dimer using an accurate coarse-grained force field coupled to Hamiltonian-temperature replica exchange molecular dynamics. The D23N variant impedes the salt-bridge formation between D23 and K28 seen in the wild-type A beta, leading to very different fibrillation properties and final amyloid fibrils. Our results show that the A beta(1-42) dimer has a higher propensity than the A beta(1-40), dimer to form beta-strands at the central hydrophobic core (residues 17-21) and at the C-terminal (residues 30-42), which are two segments crucial to the oligomerization of A beta. The free energy landscape of the A beta(1-42) dimer is also broader and more complex than that of the A beta(1-40) dimer. Interestingly, D23N also impacts the free energy landscape by increasing the population of configurations with higher beta-strand propensities when compared against A beta(40). In addition, while A beta(1-40)(D23N) displays a higher beta-strand propensity at the C-terminal, its solvent accessibility does not change with respect to the wild-type sequence. Overall, our results show the strong impact of the two amino acids Ile41-Ala42 and the salt-bridge D23-K28 on the folding of the A beta dimer.