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Block #116,847

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/14/2013, 4:36:07 PM Β· Difficulty 9.7493 Β· 6,682,679 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
207736fceddd63b13bc3ae96d9cba804275261557445011a31c156c33df15e54
View on Chainz β†—

Height

#116,847

Difficulty

9.749273

Transactions

1

Size

199 B

Version

2

Bits

09bfd053

Nonce

210,402

Timestamp

8/14/2013, 4:36:07 PM

Confirmations

6,682,679

Mined by

⛏️ P2SHAT3dRckguQx6f5eEEVjWX7iYBwiggfceho

Merkle Root

226b42ba08d9cf2191eefed760bc951503382b1705fad2a958d2ea017cd6888d
Transactions (1)
Coinbase226b42ba08d9cf…d2ea017cd6888d
1 in β†’ 1 out10.5100 XPM109 B
AT3dRckg…iggfceho
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.

8.749 Γ— 10⁹⁴(95-digit number)
87495121479426676682…10047836021172915941
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
8.749 Γ— 10⁹⁴(95-digit number)
87495121479426676682…10047836021172915941
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.749 Γ— 10⁹⁡(96-digit number)
17499024295885335336…20095672042345831881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.499 Γ— 10⁹⁡(96-digit number)
34998048591770670673…40191344084691663761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.999 Γ— 10⁹⁡(96-digit number)
69996097183541341346…80382688169383327521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.399 Γ— 10⁹⁢(97-digit number)
13999219436708268269…60765376338766655041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.799 Γ— 10⁹⁢(97-digit number)
27998438873416536538…21530752677533310081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.599 Γ— 10⁹⁢(97-digit number)
55996877746833073076…43061505355066620161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.119 Γ— 10⁹⁷(98-digit number)
11199375549366614615…86123010710133240321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.239 Γ— 10⁹⁷(98-digit number)
22398751098733229230…72246021420266480641
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:57,640,257 XPMΒ·at block #6,799,525 Β· updates every 60s
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