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Summary of Significant Accounting Policies - Revenue Recognition (Details)	9 Months Ended
	Sep. 30, 2021 item
Summary of Significant Accounting Policies
Number of performance obligation	1
Revenue, Practical Expedient [Abstract]
Financing component	true

X

- Definition

The threshold number of performance obligation to allocate transaction price.

+ References

No definition available.

+ Details

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Namespace Prefix:	ptgx_
Data Type:	xbrli:integerItemType
Balance Type:	na
Period Type:	duration

X

- References

No definition available.

+ Details

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

X

- References

No definition available.

+ Details

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

X

- Definition

Indicates (true false) whether practical expedient was elected not to adjust consideration for effect of financing component when transfer and customer payment for product or service occurs within one year or less.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 606
-SubTopic 10
-Section 50
-Paragraph 22
-URI http://asc.fasb.org/extlink&oid=121604090&loc=SL49130569-203045

+ Details

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Namespace Prefix:	us-gaap_
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Balance Type:	na
Period Type:	duration