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Home/Chain Registry/Block #566,687

Block #566,687

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/29/2014, 2:16:12 AM Β· Difficulty 10.9661 Β· 6,234,141 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a993736c1e7b93bc2cdb8360c5ea397e170b20e825b8bdc2991f1e88f8aecfa1
View on Chainz β†—

Height

#566,687

Difficulty

10.966072

Transactions

1

Size

208 B

Version

2

Bits

0af75084

Nonce

373,483,891

Timestamp

5/29/2014, 2:16:12 AM

Confirmations

6,234,141

Merkle Root

f078c7e8883d12f2c3ccdaa9cd361a5a4f7d8ba846c0cffd48876128ea05b937
Transactions (1)
Coinbasef078c7e8883d12…876128ea05b937
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.

1.965 Γ— 10¹⁰⁰(101-digit number)
19659015239084289602…39650646073881359360
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
1.965 Γ— 10¹⁰⁰(101-digit number)
19659015239084289602…39650646073881359361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.931 Γ— 10¹⁰⁰(101-digit number)
39318030478168579205…79301292147762718721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.863 Γ— 10¹⁰⁰(101-digit number)
78636060956337158410…58602584295525437441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.572 Γ— 10¹⁰¹(102-digit number)
15727212191267431682…17205168591050874881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.145 Γ— 10¹⁰¹(102-digit number)
31454424382534863364…34410337182101749761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.290 Γ— 10¹⁰¹(102-digit number)
62908848765069726728…68820674364203499521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.258 Γ— 10¹⁰²(103-digit number)
12581769753013945345…37641348728406999041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.516 Γ— 10¹⁰²(103-digit number)
25163539506027890691…75282697456813998081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.032 Γ— 10¹⁰²(103-digit number)
50327079012055781382…50565394913627996161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.006 Γ— 10¹⁰³(104-digit number)
10065415802411156276…01130789827255992321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.013 Γ— 10¹⁰³(104-digit number)
20130831604822312553…02261579654511984641
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 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.

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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 566687

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 a993736c1e7b93bc2cdb8360c5ea397e170b20e825b8bdc2991f1e88f8aecfa1

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 #566,687 on Chainz β†—
Circulating Supply:57,650,681 XPMΒ·at block #6,800,827 Β· updates every 60s
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