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Block #236,260

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/31/2013, 10:00:18 AM Β· Difficulty 9.9470 Β· 6,559,204 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ef733e569bae97e6f06c8cdd28dfd128b09cac6931732f02d5efefce9e990859
View on Chainz β†—

Height

#236,260

Difficulty

9.946991

Transactions

1

Size

199 B

Version

2

Bits

09f26dfe

Nonce

95,156

Timestamp

10/31/2013, 10:00:18 AM

Confirmations

6,559,204

Mined by

⛏️ P2SHAc9dvttfeWkjeWCeTL35pvC4fg9FoHtp6K

Merkle Root

31e4858079c7be614338346068a2ccabb5bffc3ede96ec6cabab8c50b4ed1827
Transactions (1)
Coinbase31e4858079c7be…ab8c50b4ed1827
1 in β†’ 1 out10.0900 XPM109 B
Ac9dvttf…9FoHtp6K
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.

2.985 Γ— 10⁹⁴(95-digit number)
29858235969647932505…34485119770280460721
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
2.985 Γ— 10⁹⁴(95-digit number)
29858235969647932505…34485119770280460721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.971 Γ— 10⁹⁴(95-digit number)
59716471939295865011…68970239540560921441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.194 Γ— 10⁹⁡(96-digit number)
11943294387859173002…37940479081121842881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.388 Γ— 10⁹⁡(96-digit number)
23886588775718346004…75880958162243685761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.777 Γ— 10⁹⁡(96-digit number)
47773177551436692009…51761916324487371521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.554 Γ— 10⁹⁡(96-digit number)
95546355102873384018…03523832648974743041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.910 Γ— 10⁹⁢(97-digit number)
19109271020574676803…07047665297949486081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.821 Γ— 10⁹⁢(97-digit number)
38218542041149353607…14095330595898972161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.643 Γ— 10⁹⁢(97-digit number)
76437084082298707214…28190661191797944321
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:57,607,771 XPMΒ·at block #6,795,463 Β· updates every 60s
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