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Block #82,112

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/25/2013, 4:58:20 AM Β· Difficulty 9.2749 Β· 6,713,553 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3f5a8653845afa41a5752ec8c66af89cc6fc0ba40b4195b7dff149bce69f74ff
View on Chainz β†—

Height

#82,112

Difficulty

9.274934

Transactions

2

Size

537 B

Version

2

Bits

09466213

Nonce

9,698

Timestamp

7/25/2013, 4:58:20 AM

Confirmations

6,713,553

Mined by

⛏️ P2SHAWJdVGNZVs7WzQCgruhoiM1zpcEKN6upBd

Merkle Root

1d9fa586ca2ad208607f65c189f5f52c3a309ac44d23c6fa07feee2aa6f14e5d
Transactions (2)
Coinbased5d0f671751f54…6c131f64855b2d
1 in β†’ 1 out11.6200 XPM109 B
AWJdVGNZ…EKN6upBd
f9e50ef77c2ec4…857c59e6ecde22
2 in β†’ 1 out100.0000 XPM339 B
AKKb38vw…nN1DKpfW
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.

2.363 Γ— 10⁹³(94-digit number)
23632598464313248620…68786116735427638201
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
2.363 Γ— 10⁹³(94-digit number)
23632598464313248620…68786116735427638201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.726 Γ— 10⁹³(94-digit number)
47265196928626497241…37572233470855276401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.453 Γ— 10⁹³(94-digit number)
94530393857252994483…75144466941710552801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.890 Γ— 10⁹⁴(95-digit number)
18906078771450598896…50288933883421105601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.781 Γ— 10⁹⁴(95-digit number)
37812157542901197793…00577867766842211201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.562 Γ— 10⁹⁴(95-digit number)
75624315085802395586…01155735533684422401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.512 Γ— 10⁹⁡(96-digit number)
15124863017160479117…02311471067368844801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.024 Γ— 10⁹⁡(96-digit number)
30249726034320958234…04622942134737689601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.049 Γ— 10⁹⁡(96-digit number)
60499452068641916469…09245884269475379201
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 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 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,609,385 XPMΒ·at block #6,795,664 Β· updates every 60s
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