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Home/Chain Registry/Block #566,719

Block #566,719

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/29/2014, 2:51:42 AM Β· Difficulty 10.9660 Β· 6,227,871 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ca9969b9c892e3d0e7b279581edd5f4f3818e8e2d6e379c4ff00d3294e5704f3
View on Chainz β†—

Height

#566,719

Difficulty

10.966050

Transactions

1

Size

207 B

Version

2

Bits

0af74f0a

Nonce

217,873,654

Timestamp

5/29/2014, 2:51:42 AM

Confirmations

6,227,871

Merkle Root

ebf174910a303af8a9b15c7534c8572636792b13979b9a38d9d55676b5196174
Transactions (1)
Coinbaseebf174910a303a…d55676b5196174
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.

8.700 Γ— 10⁹⁢(97-digit number)
87005175276960011352…47045604990342808170
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
8.700 Γ— 10⁹⁢(97-digit number)
87005175276960011352…47045604990342808169
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.740 Γ— 10⁹⁷(98-digit number)
17401035055392002270…94091209980685616339
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.480 Γ— 10⁹⁷(98-digit number)
34802070110784004541…88182419961371232679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.960 Γ— 10⁹⁷(98-digit number)
69604140221568009082…76364839922742465359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.392 Γ— 10⁹⁸(99-digit number)
13920828044313601816…52729679845484930719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.784 Γ— 10⁹⁸(99-digit number)
27841656088627203632…05459359690969861439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.568 Γ— 10⁹⁸(99-digit number)
55683312177254407265…10918719381939722879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.113 Γ— 10⁹⁹(100-digit number)
11136662435450881453…21837438763879445759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.227 Γ— 10⁹⁹(100-digit number)
22273324870901762906…43674877527758891519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.454 Γ— 10⁹⁹(100-digit number)
44546649741803525812…87349755055517783039
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 566719

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 ca9969b9c892e3d0e7b279581edd5f4f3818e8e2d6e379c4ff00d3294e5704f3

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 #566,719 on Chainz β†—
Circulating Supply:57,600,760 XPMΒ·at block #6,794,589 Β· updates every 60s
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