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Block #87,937

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/29/2013, 6:23:57 AM Β· Difficulty 9.2723 Β· 6,721,289 confirmations

1CC
Cunningham Chain of the First Kind

A sequence where each prime is double the previous prime plus one.

Block Header
Block Hash
94954add0177cdc27a24e6b0a15dbac4869229dd7a0ebece11232d2b5c03ba17
View on Chainz β†—

Height

#87,937

Difficulty

9.272278

Transactions

1

Size

205 B

Version

2

Bits

0945b407

Nonce

10

Timestamp

7/29/2013, 6:23:57 AM

Confirmations

6,721,289

Mined by

⛏️ P2SHAN239ZSez8P7hPVhXmS7NxVWfRPHfu9UZq

Merkle Root

139fce76ccdeb7f35c4008384556bc98f8a7ef5458f5d3fa077bca249c60f60b
Transactions (1)
Coinbase139fce76ccdeb7…7bca249c60f60b
1 in β†’ 1 out11.6100 XPM110 B
AN239ZSe…PHfu9UZq
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.717 Γ— 10¹⁰⁷(108-digit number)
17172527427216256084…30189861960389138849
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

1
origin βˆ’ 1
1.717 Γ— 10¹⁰⁷(108-digit number)
17172527427216256084…30189861960389138849
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.434 Γ— 10¹⁰⁷(108-digit number)
34345054854432512168…60379723920778277699
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.869 Γ— 10¹⁰⁷(108-digit number)
68690109708865024337…20759447841556555399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.373 Γ— 10¹⁰⁸(109-digit number)
13738021941773004867…41518895683113110799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.747 Γ— 10¹⁰⁸(109-digit number)
27476043883546009734…83037791366226221599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.495 Γ— 10¹⁰⁸(109-digit number)
54952087767092019469…66075582732452443199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.099 Γ— 10¹⁰⁹(110-digit number)
10990417553418403893…32151165464904886399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.198 Γ— 10¹⁰⁹(110-digit number)
21980835106836807787…64302330929809772799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.396 Γ— 10¹⁰⁹(110-digit number)
43961670213673615575…28604661859619545599
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 consecutive prime numbers forming a Cunningham Chain of the First Kind. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜†β˜†β˜†β˜†
Rarity
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,717,871 XPMΒ·at block #6,809,225 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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