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Home/Chain Registry/Block #566,789

Block #566,789

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/29/2014, 4:14:08 AM Β· Difficulty 10.9660 Β· 6,260,355 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7171e215c084295feff2d1a6d20bbe449967334f10126c4abe38e0611bc3b282
View on Chainz β†—

Height

#566,789

Difficulty

10.965959

Transactions

1

Size

207 B

Version

2

Bits

0af74913

Nonce

297,140,428

Timestamp

5/29/2014, 4:14:08 AM

Confirmations

6,260,355

Merkle Root

138786c2c234d42d8f629706eef92a49b02031569b89e71fa9ef3fe3ce9af5f9
Transactions (1)
Coinbase138786c2c234d4…ef3fe3ce9af5f9
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.

1.394 Γ— 10⁹⁷(98-digit number)
13941311402842325402…22526743343967834200
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
1.394 Γ— 10⁹⁷(98-digit number)
13941311402842325402…22526743343967834199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.788 Γ— 10⁹⁷(98-digit number)
27882622805684650804…45053486687935668399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.576 Γ— 10⁹⁷(98-digit number)
55765245611369301608…90106973375871336799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.115 Γ— 10⁹⁸(99-digit number)
11153049122273860321…80213946751742673599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.230 Γ— 10⁹⁸(99-digit number)
22306098244547720643…60427893503485347199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.461 Γ— 10⁹⁸(99-digit number)
44612196489095441287…20855787006970694399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.922 Γ— 10⁹⁸(99-digit number)
89224392978190882574…41711574013941388799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.784 Γ— 10⁹⁹(100-digit number)
17844878595638176514…83423148027882777599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.568 Γ— 10⁹⁹(100-digit number)
35689757191276353029…66846296055765555199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.137 Γ— 10⁹⁹(100-digit number)
71379514382552706059…33692592111531110399
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 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
UncommonChain length 10
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 566789

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 7171e215c084295feff2d1a6d20bbe449967334f10126c4abe38e0611bc3b282

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 #566,789 on Chainz β†—
Circulating Supply:57,861,334 XPMΒ·at block #6,827,143 Β· updates every 60s
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