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Block #575,685

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/4/2014, 2:54:31 AM Β· Difficulty 10.9684 Β· 6,219,695 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
fd0da57747339b4491aa59591ff2363befc7df3487f82443c7d73f7c5a13065b
View on Chainz β†—

Height

#575,685

Difficulty

10.968429

Transactions

2

Size

435 B

Version

2

Bits

0af7eafa

Nonce

207,832,717

Timestamp

6/4/2014, 2:54:31 AM

Confirmations

6,219,695

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

bf98f252896dfa45bfa368c034b1ade78f0fc3566f5889c216f769f1788e4f7b
Transactions (2)
Coinbase041142a011e9b6…9a6ec71dedddaa
1 in β†’ 1 out8.3100 XPM116 B
ANSXnLY2…Sd25TjkD
732d9ef70615ac…25e1d5456ec6b3
1 in β†’ 2 out7.2710 XPM227 B
AQYfM6tR…wtD7VsKoASjQR9Yf…73983G2U
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.

4.152 Γ— 10⁹⁸(99-digit number)
41521776423548355784…09218233380030621121
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
4.152 Γ— 10⁹⁸(99-digit number)
41521776423548355784…09218233380030621121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.304 Γ— 10⁹⁸(99-digit number)
83043552847096711569…18436466760061242241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.660 Γ— 10⁹⁹(100-digit number)
16608710569419342313…36872933520122484481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.321 Γ— 10⁹⁹(100-digit number)
33217421138838684627…73745867040244968961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.643 Γ— 10⁹⁹(100-digit number)
66434842277677369255…47491734080489937921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.328 Γ— 10¹⁰⁰(101-digit number)
13286968455535473851…94983468160979875841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.657 Γ— 10¹⁰⁰(101-digit number)
26573936911070947702…89966936321959751681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.314 Γ— 10¹⁰⁰(101-digit number)
53147873822141895404…79933872643919503361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.062 Γ— 10¹⁰¹(102-digit number)
10629574764428379080…59867745287839006721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.125 Γ— 10¹⁰¹(102-digit number)
21259149528856758161…19735490575678013441
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:57,607,098 XPMΒ·at block #6,795,379 Β· updates every 60s
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