This paper investigates the number of neighbors each node in a wireless network must connect to in order for the network to be connected. Unlike wired networks, wireless networks do not have pre-existing links; instead, links are formed by nodes choosing neighbors to connect to. The study shows that for a network with n randomly placed nodes, each node should connect to Θ(log n) nearest neighbors to ensure connectivity. If each node connects to less than 0.074 log n nearest neighbors, the network is asymptotically disconnected with probability one as n increases. Conversely, if each node connects to more than 5.1774 log n nearest neighbors, the network is asymptotically connected with probability approaching one as n increases. These results contrast with earlier works in the 1970s and 1980s that suggested the "magic number" of nearest neighbors should be six or eight. The paper also discusses the trade-off between network connectivity and capacity. While more links can improve connectivity, they may also increase interference, reducing network capacity. The study shows that the number of neighbors each node must connect to grows like Θ(log n) for the network to be connected. The results are derived from a rigorous analysis of the network's connectivity properties and are supported by simulations. The paper is organized into sections that present the problem formulation, main result, proof of the main result, simulation results, and conclusion. The main result is that Θ(log n) neighbors are necessary and sufficient for asymptotic connectivity. The paper also discusses the implications of these results for wireless networks and highlights the importance of considering both connectivity and capacity in network design.This paper investigates the number of neighbors each node in a wireless network must connect to in order for the network to be connected. Unlike wired networks, wireless networks do not have pre-existing links; instead, links are formed by nodes choosing neighbors to connect to. The study shows that for a network with n randomly placed nodes, each node should connect to Θ(log n) nearest neighbors to ensure connectivity. If each node connects to less than 0.074 log n nearest neighbors, the network is asymptotically disconnected with probability one as n increases. Conversely, if each node connects to more than 5.1774 log n nearest neighbors, the network is asymptotically connected with probability approaching one as n increases. These results contrast with earlier works in the 1970s and 1980s that suggested the "magic number" of nearest neighbors should be six or eight. The paper also discusses the trade-off between network connectivity and capacity. While more links can improve connectivity, they may also increase interference, reducing network capacity. The study shows that the number of neighbors each node must connect to grows like Θ(log n) for the network to be connected. The results are derived from a rigorous analysis of the network's connectivity properties and are supported by simulations. The paper is organized into sections that present the problem formulation, main result, proof of the main result, simulation results, and conclusion. The main result is that Θ(log n) neighbors are necessary and sufficient for asymptotic connectivity. The paper also discusses the implications of these results for wireless networks and highlights the importance of considering both connectivity and capacity in network design.