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Note 7 - Stockholders' Equity (Details Textual) - USD ($)
3 Months Ended 12 Months Ended
Jun. 14, 2017
Jul. 22, 2016
Sep. 30, 2017
Dec. 31, 2017
Dec. 31, 2016
Apr. 19, 2017
Dec. 31, 2015
Proceeds from Issuance or Sale of Equity $ 18,200,000            
Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding, Number       1,166,709 691,374   691,374
Share-based Compensation Arrangement by Share-based Payment Award, Options, Grants in Period, Gross       283,372      
Share-based Compensation Arrangements by Share-based Payment Award, Options, Grants in Period, Weighted Average Exercise Price       $ 6.75      
Employee Service Share-based Compensation, Nonvested Awards, Compensation Not yet Recognized, Stock Options       $ 1,400,000      
Employee Service Share-based Compensation, Nonvested Awards, Compensation Cost Not yet Recognized, Period for Recognition       1 year 328 days      
Allocated Share-based Compensation Expense       $ 1,624,411 $ 2,471,789    
General and Administrative Expense [Member]              
Allocated Share-based Compensation Expense       1,623,056      
Research and Development Expense [Member]              
Allocated Share-based Compensation Expense       $ 1,355      
Old PLx Omnibus Stock Option Plan and Dipexium 2013 Equity Incentive Plan [Member]              
Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding, Number           191,963  
Share-based Compensation Arrangement by Share-based Payment Award, Number of Shares Available for Grant       242,903      
Old PLx Omnibus Stock Option Plan and Dipexium 2013 Equity Incentive Plan [Member] | Employees [Member] | Employee Stock Option [Member]              
Share-based Compensation Arrangement by Share-based Payment Award, Fair Value Assumptions, Expected Dividend Rate       0.00%      
Old PLx Omnibus Stock Option Plan and Dipexium 2013 Equity Incentive Plan [Member] | Employees [Member] | Employee Stock Option [Member] | Minimum [Member]              
Share-based Compensation Arrangement by Share-based Payment Award, Fair Value Assumptions, Expected Volatility Rate       75.00%      
Old PLx Omnibus Stock Option Plan and Dipexium 2013 Equity Incentive Plan [Member] | Employees [Member] | Employee Stock Option [Member] | Maximum [Member]              
Share-based Compensation Arrangement by Share-based Payment Award, Fair Value Assumptions, Expected Volatility Rate       86.00%      
Old PLx Omnibus Stock Option Plan and Dipexium 2013 Equity Incentive Plan [Member] | Former Officer [Member]              
Share-based Compensation Arrangement by Share-based Payment Award, Plan Modification, Incremental Compensation Cost     $ 150,000        
Allocated Share-based Compensation Expense     $ 200,000        
Old PLx Omnibus Stock Option Plan and Dipexium 2013 Equity Incentive Plan [Member] | Director [Member]              
Stock Issued During Period, Shares, Share-based Compensation, Gross     30,000        
Omnibus Stock Option Plan [Member] | Executives [Member]              
Share-based Compensation Arrangement by Share-based Payment Award, Options, Vested, Number of Shares   118,134          
Share-based Compensation Arrangement by Share-based Payment Award, Options, Vested in Period, Fair Value   $ 948,117          
Fair Value Inputs, Discount Rate   1.24%          
Share-based Compensation Arrangement by Share-based Payment Award, Fair Value Assumptions, Expected Term   4 years 251 days          
Share-based Compensation Arrangement by Share-based Payment Award, Fair Value Assumptions, Expected Volatility Rate   83.52%          
Share-based Compensation Arrangement by Share-based Payment Award, Fair Value Assumptions, Expected Dividend Rate   0.00%          
Omnibus Stock Option Plan [Member] | Employees [Member]              
Share-based Compensation Arrangement by Share-based Payment Award, Options, Grants in Period, Gross       283,372      
Share-based Compensation Arrangements by Share-based Payment Award, Options, Grants in Period, Weighted Average Exercise Price       $ 6.75      
Share-based Compensation Arrangement by Share-based Payment Award, Options, Granted in Period, Fair Value       $ 1,300,000      
Omnibus Stock Option Plan [Member] | Employees [Member] | Employee Stock Option [Member] | Minimum [Member]              
Fair Value Inputs, Discount Rate       1.20%      
Share-based Compensation Arrangement by Share-based Payment Award, Fair Value Assumptions, Expected Term       4 years 255 days      
Omnibus Stock Option Plan [Member] | Employees [Member] | Employee Stock Option [Member] | Maximum [Member]              
Fair Value Inputs, Discount Rate       2.10%      
Share-based Compensation Arrangement by Share-based Payment Award, Fair Value Assumptions, Expected Term       8 years      
June 2017 Warrants [Member]              
Class of Warrant or Right, Term 10 years            
Common Stock [Member]              
Stock Issued During Period, Shares, New Issues       2,646,091      
Stock Issued During Period, Shares, Share-based Compensation, Gross       30,000      
Public Offering [Member] | Common Stock [Member]              
Stock Issued During Period, Shares, New Issues 2,646,091            
Share Price $ 6.875            
Private Placement [Member] | June 2017 Warrants [Member]              
Class of Warrant or Right, Number of Securities Called by Warrants or Rights 2,646,091            
Class of Warrant or Right, Exercise Price of Warrants or Rights $ 7.50