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Block #571,233

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/1/2014, 8:40:03 AM Β· Difficulty 10.9651 Β· 6,228,018 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f75de320c309fca4c2e62d1d01e93c46096da8c54db3fe5822bd649969594e75
View on Chainz β†—

Height

#571,233

Difficulty

10.965149

Transactions

1

Size

208 B

Version

2

Bits

0af713fd

Nonce

1,005,296,776

Timestamp

6/1/2014, 8:40:03 AM

Confirmations

6,228,018

Merkle Root

43ab27bad292c813fb30bc26a0b2868ea43d626a4fbaa1dd9b17570910e4ca5a
Transactions (1)
Coinbase43ab27bad292c8…17570910e4ca5a
1 in β†’ 1 out8.3000 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.

2.106 Γ— 10⁹⁸(99-digit number)
21068973567387415583…42384718834269025280
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
2.106 Γ— 10⁹⁸(99-digit number)
21068973567387415583…42384718834269025279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.213 Γ— 10⁹⁸(99-digit number)
42137947134774831167…84769437668538050559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.427 Γ— 10⁹⁸(99-digit number)
84275894269549662334…69538875337076101119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.685 Γ— 10⁹⁹(100-digit number)
16855178853909932466…39077750674152202239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.371 Γ— 10⁹⁹(100-digit number)
33710357707819864933…78155501348304404479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.742 Γ— 10⁹⁹(100-digit number)
67420715415639729867…56311002696608808959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.348 Γ— 10¹⁰⁰(101-digit number)
13484143083127945973…12622005393217617919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.696 Γ— 10¹⁰⁰(101-digit number)
26968286166255891946…25244010786435235839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.393 Γ— 10¹⁰⁰(101-digit number)
53936572332511783893…50488021572870471679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.078 Γ— 10¹⁰¹(102-digit number)
10787314466502356778…00976043145740943359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.157 Γ— 10¹⁰¹(102-digit number)
21574628933004713557…01952086291481886719
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Cunningham Chain of the First 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.

View full Prime Chain Discovery page β†’
β˜…β˜…β˜…β˜†β˜†
Rarity
RareChain length 11
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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height
getblockhash 571233

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data
getblock f75de320c309fca4c2e62d1d01e93c46096da8c54db3fe5822bd649969594e75

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help β†’ Debug Window β†’ Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #571,233 on Chainz β†—
Circulating Supply:57,638,047 XPMΒ·at block #6,799,250 Β· updates every 60s
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