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Block #575,058

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/3/2014, 5:36:49 PM Β· Difficulty 10.9680 Β· 6,219,308 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2c792f4d507b93124cfb4186bef50b6690bfa65293097688732f8c47e2422a0f
View on Chainz β†—

Height

#575,058

Difficulty

10.967973

Transactions

1

Size

243 B

Version

2

Bits

0af7cd1c

Nonce

1,109,744,694

Timestamp

6/3/2014, 5:36:49 PM

Confirmations

6,219,308

Mined by

⛏️ P2SHAXn1KW6PTFKBcGVcbZ8CPoUc4Pc7VDu2zv

Merkle Root

df1534b7de59af2b478c15f35abdf8b81ff4a853531ab868fc6797f5ca72bba8
Transactions (1)
Coinbasedf1534b7de59af…6797f5ca72bba8
1 in β†’ 2 out8.3000 XPM152 B
AXn1KW6P…c7VDu2zvALPu3s2c…EJXLjVFh
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.

4.019 Γ— 10⁹⁷(98-digit number)
40199433263696966981…41781208376031174801
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
4.019 Γ— 10⁹⁷(98-digit number)
40199433263696966981…41781208376031174801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.039 Γ— 10⁹⁷(98-digit number)
80398866527393933963…83562416752062349601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.607 Γ— 10⁹⁸(99-digit number)
16079773305478786792…67124833504124699201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.215 Γ— 10⁹⁸(99-digit number)
32159546610957573585…34249667008249398401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.431 Γ— 10⁹⁸(99-digit number)
64319093221915147171…68499334016498796801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.286 Γ— 10⁹⁹(100-digit number)
12863818644383029434…36998668032997593601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.572 Γ— 10⁹⁹(100-digit number)
25727637288766058868…73997336065995187201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.145 Γ— 10⁹⁹(100-digit number)
51455274577532117736…47994672131990374401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.029 Γ— 10¹⁰⁰(101-digit number)
10291054915506423547…95989344263980748801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.058 Γ— 10¹⁰⁰(101-digit number)
20582109831012847094…91978688527961497601
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,598,962 XPMΒ·at block #6,794,365 Β· updates every 60s
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