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Block #73,686

2CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/21/2013, 7:14:01 AM Β· Difficulty 8.9950 Β· 6,720,901 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
80d89ad8d7bf0b625ea23763c92cd55c54c9bb9b64b175be57fa2f5b2b2387e3
View on Chainz β†—

Height

#73,686

Difficulty

8.995002

Transactions

1

Size

197 B

Version

2

Bits

08feb86f

Nonce

659

Timestamp

7/21/2013, 7:14:01 AM

Confirmations

6,720,901

Mined by

⛏️ P2SHAZDgU5ryLDBgQ43WTK1SQdESypdmcwdqVC

Merkle Root

ac13997ad99e1745aeb627c05bd3885e7185df6e9129a517318ae88ba3542fef
Transactions (1)
Coinbaseac13997ad99e17…8ae88ba3542fef
1 in β†’ 1 out12.3400 XPM109 B
AZDgU5ry…dmcwdqVC
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.

6.860 Γ— 10⁸⁹(90-digit number)
68605992367833245100…80906168845227880201
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
6.860 Γ— 10⁸⁹(90-digit number)
68605992367833245100…80906168845227880201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.372 Γ— 10⁹⁰(91-digit number)
13721198473566649020…61812337690455760401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.744 Γ— 10⁹⁰(91-digit number)
27442396947133298040…23624675380911520801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.488 Γ— 10⁹⁰(91-digit number)
54884793894266596080…47249350761823041601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.097 Γ— 10⁹¹(92-digit number)
10976958778853319216…94498701523646083201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.195 Γ— 10⁹¹(92-digit number)
21953917557706638432…88997403047292166401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.390 Γ— 10⁹¹(92-digit number)
43907835115413276864…77994806094584332801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.781 Γ— 10⁹¹(92-digit number)
87815670230826553729…55989612189168665601
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 8 consecutive prime numbers forming a Cunningham Chain of the Second 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 8

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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,600,743 XPMΒ·at block #6,794,586 Β· updates every 60s
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