1031 Exchange to Purchase Primary Residence

[Dane Price]

I have a rental property that I have decided to sell as it is no longer a lucrative cashflow opportunity. The property was originally purchased 4 years ago as our primary residence, but decided to move out and rent the property after 16 months as our primary residence. Obviously we knew nothing about investing at the time and have basically ruined our chances of making any tax free capitol gains on the sell (2 year primary residence of past 5 years rule), so now I would like to figure out my options using a 1031 exchange to defer taxes. I understand the idea of purchasing a new investment property of equal or greater value as the 1031 exchange property, but I was wondering of this other scenario is legitimate.

Can I sell my rental property and my current primary residence (lived here for 3 years), then purchase a new primary residence and use a 1031 exchange from the rental property profit on the new primary resident? I realize there is a whole lot of coordination that must be done in the 180 days allotted under the 1031, but is it legal to use the 1031 to assist purchase of a primary residence and not an investment property?