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Block #214,812

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/17/2013, 5:13:49 PM Β· Difficulty 9.9241 Β· 6,590,277 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
dfcb9fece9b7873b84395657d8210b67623dce48db92ece6f02b1838e7a5d066
View on Chainz β†—

Height

#214,812

Difficulty

9.924144

Transactions

1

Size

197 B

Version

2

Bits

09ec94ac

Nonce

114,371

Timestamp

10/17/2013, 5:13:49 PM

Confirmations

6,590,277

Mined by

⛏️ P2SHARBvr1evuYzdjmXQBMTxCmA4hCNg7YPkPH

Merkle Root

a32cd4f09bd364f008269f76f80fe0432109caf06dc34966b91b8bb9f1021de2
Transactions (1)
Coinbasea32cd4f09bd364…1b8bb9f1021de2
1 in β†’ 1 out10.1400 XPM109 B
ARBvr1ev…Ng7YPkPH
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.

4.315 Γ— 10⁸⁸(89-digit number)
43151791594176730970…34402720059693745701
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
4.315 Γ— 10⁸⁸(89-digit number)
43151791594176730970…34402720059693745701
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.630 Γ— 10⁸⁸(89-digit number)
86303583188353461941…68805440119387491401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.726 Γ— 10⁸⁹(90-digit number)
17260716637670692388…37610880238774982801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.452 Γ— 10⁸⁹(90-digit number)
34521433275341384776…75221760477549965601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.904 Γ— 10⁸⁹(90-digit number)
69042866550682769552…50443520955099931201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.380 Γ— 10⁹⁰(91-digit number)
13808573310136553910…00887041910199862401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.761 Γ— 10⁹⁰(91-digit number)
27617146620273107821…01774083820399724801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.523 Γ— 10⁹⁰(91-digit number)
55234293240546215642…03548167640799449601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.104 Γ— 10⁹¹(92-digit number)
11046858648109243128…07096335281598899201
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:57,684,777 XPMΒ·at block #6,805,088 Β· updates every 60s
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