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Summary of Significant Accounting Policies - Concentrations of Credit Risk (Details)	Sep. 30, 2021 Institution
Summary of Significant Accounting Policies
Number of financial institutions at which cash is held	2

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- Definition

The number of financial institutions that hold the entity's cash.

+ References

No definition available.

+ Details

Name:	ptgx_CashNumberOfFinancialInstitutions
Namespace Prefix:	ptgx_
Data Type:	xbrli:integerItemType
Balance Type:	na
Period Type:	instant

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- References

No definition available.

+ Details

Name:	us-gaap_AccountingPoliciesAbstract
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration