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Block #582,958

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/10/2014, 4:11:28 AM Β· Difficulty 10.9583 Β· 6,243,758 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2767ec16be5ea772b268b0f549d7f52ddc27318caa010eb10e471c262deede31
View on Chainz β†—

Height

#582,958

Difficulty

10.958252

Transactions

1

Size

208 B

Version

2

Bits

0af55004

Nonce

1,423,149,996

Timestamp

6/10/2014, 4:11:28 AM

Confirmations

6,243,758

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

c6b30ec3c8b1b4c5533ed8500cde723091bd02c2759db4b18c3a95bae2519243
Transactions (1)
Coinbasec6b30ec3c8b1b4…3a95bae2519243
1 in β†’ 1 out8.3100 XPM116 B
ANSXnLY2…Sd25TjkD
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.

7.021 Γ— 10⁹⁹(100-digit number)
70216703091259628920…05701012270758318081
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
7.021 Γ— 10⁹⁹(100-digit number)
70216703091259628920…05701012270758318081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.404 Γ— 10¹⁰⁰(101-digit number)
14043340618251925784…11402024541516636161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.808 Γ— 10¹⁰⁰(101-digit number)
28086681236503851568…22804049083033272321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.617 Γ— 10¹⁰⁰(101-digit number)
56173362473007703136…45608098166066544641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.123 Γ— 10¹⁰¹(102-digit number)
11234672494601540627…91216196332133089281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.246 Γ— 10¹⁰¹(102-digit number)
22469344989203081254…82432392664266178561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.493 Γ— 10¹⁰¹(102-digit number)
44938689978406162509…64864785328532357121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.987 Γ— 10¹⁰¹(102-digit number)
89877379956812325018…29729570657064714241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.797 Γ— 10¹⁰²(103-digit number)
17975475991362465003…59459141314129428481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.595 Γ— 10¹⁰²(103-digit number)
35950951982724930007…18918282628258856961
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:57,857,881 XPMΒ·at block #6,826,715 Β· updates every 60s
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