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  <xs:element id="prme_ResearchAndDevelopmentExpenseResearchCosts" abstract="false" name="ResearchAndDevelopmentExpenseResearchCosts" nillable="true" xbrli:periodType="duration" xbrli:balance="debit" substitutionGroup="xbrli:item" type="xbrli:monetaryItemType"/>
  <xs:element id="prme_GeneralAndAdministrativeExpensePersonnelExpenses" abstract="false" name="GeneralAndAdministrativeExpensePersonnelExpenses" nillable="true" xbrli:periodType="duration" xbrli:balance="debit" substitutionGroup="xbrli:item" type="xbrli:monetaryItemType"/>
  <xs:element id="prme_USTreasuryBillsAndGovernmentSecuritiesMember" abstract="true" name="USTreasuryBillsAndGovernmentSecuritiesMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="prme_LaboratoryEquipmentMember" abstract="true" name="LaboratoryEquipmentMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="prme_AccruedResearchAndClinicalCostsCurrent" abstract="false" name="AccruedResearchAndClinicalCostsCurrent" nillable="true" xbrli:periodType="instant" xbrli:balance="credit" substitutionGroup="xbrli:item" type="xbrli:monetaryItemType"/>
  <xs:element id="prme_AccruedLicenseFeeCurrent" abstract="false" name="AccruedLicenseFeeCurrent" nillable="true" xbrli:periodType="instant" xbrli:balance="credit" substitutionGroup="xbrli:item" type="xbrli:monetaryItemType"/>
  <xs:element id="prme_LesseeOperatingLeaseLiabilityToBePaidAfterYearFour" abstract="false" name="LesseeOperatingLeaseLiabilityToBePaidAfterYearFour" nillable="true" xbrli:periodType="instant" xbrli:balance="credit" substitutionGroup="xbrli:item" type="xbrli:monetaryItemType"/>
  <xs:element id="prme_SalesAgreementMember" abstract="true" name="SalesAgreementMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="prme_A2023ATMProgramMember" abstract="true" name="A2023ATMProgramMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="prme_CommonStockParOrStatedValuePerShareUnderAmendment" abstract="false" name="CommonStockParOrStatedValuePerShareUnderAmendment" nillable="true" xbrli:periodType="instant" substitutionGroup="xbrli:item" type="dtr-types:perShareItemType"/>
  <xs:element id="prme_CommonStockNumberOfVotesPerShare" abstract="false" name="CommonStockNumberOfVotesPerShare" nillable="true" xbrli:periodType="instant" substitutionGroup="xbrli:item" type="xbrli:integerItemType"/>
  <xs:element id="prme_TimeBasedStockOptionsMember" abstract="true" name="TimeBasedStockOptionsMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="prme_PerformanceBasedStockOptionsMember" abstract="true" name="PerformanceBasedStockOptionsMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="prme_A2022StockOptionAndIncentivePlanMember" abstract="true" name="A2022StockOptionAndIncentivePlanMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="prme_A2022StockOptionAndIncentivePlanAnd2019EquityIncentivePlanMember" abstract="true" name="A2022StockOptionAndIncentivePlanAnd2019EquityIncentivePlanMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="prme_A2022EmployeeStockPurchasePlanMember" abstract="true" name="A2022EmployeeStockPurchasePlanMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="prme_ShareBasedCompensationArrangementByShareBasedPaymentAwardAnnualIncreaseInSharesReservedForIssuancePercentage" abstract="false" name="ShareBasedCompensationArrangementByShareBasedPaymentAwardAnnualIncreaseInSharesReservedForIssuancePercentage" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:percentItemType"/>
  <xs:element id="prme_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfAdditionalSharesAllowableUnderThePlan" abstract="false" name="ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfAdditionalSharesAllowableUnderThePlan" nillable="true" xbrli:periodType="instant" substitutionGroup="xbrli:item" type="xbrli:sharesItemType"/>
  <xs:element id="prme_JunoTherapeuticsInc.Member" abstract="true" name="JunoTherapeuticsInc.Member" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="prme_CollaborativeArrangementResearchCollaborationAndLicenseAgreementMember" abstract="true" name="CollaborativeArrangementResearchCollaborationAndLicenseAgreementMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="prme_CollaborativeArrangementRightsAndObligationsRemainingPerformanceObligation" abstract="false" name="CollaborativeArrangementRightsAndObligationsRemainingPerformanceObligation" nillable="true" xbrli:periodType="instant" xbrli:balance="credit" substitutionGroup="xbrli:item" type="xbrli:monetaryItemType"/>
</xs:schema>
