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Block #420,524

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 2/26/2014, 10:41:00 AM Β· Difficulty 10.3714 Β· 6,405,045 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4ebb9dc0d7155714eb2c09e63c409de37fceaf29f7023ace5c06ecb1e75d7155
View on Chainz β†—

Height

#420,524

Difficulty

10.371372

Transactions

1

Size

201 B

Version

2

Bits

0a5f1240

Nonce

414,054

Timestamp

2/26/2014, 10:41:00 AM

Confirmations

6,405,045

Merkle Root

1b3c3f1dc339ae1cd5a34a0ca877c739c94886cb1f8e8f9f1c4553eda20e7f99
Transactions (1)
Coinbase1b3c3f1dc339ae…4553eda20e7f99
1 in β†’ 1 out9.2800 XPM110 B
AeKNrjNj…1NEq95Ta
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.

1.089 Γ— 10⁹⁸(99-digit number)
10890426163143543499…87803005872082548480
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
1.089 Γ— 10⁹⁸(99-digit number)
10890426163143543499…87803005872082548481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.178 Γ— 10⁹⁸(99-digit number)
21780852326287086999…75606011744165096961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.356 Γ— 10⁹⁸(99-digit number)
43561704652574173999…51212023488330193921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.712 Γ— 10⁹⁸(99-digit number)
87123409305148347999…02424046976660387841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.742 Γ— 10⁹⁹(100-digit number)
17424681861029669599…04848093953320775681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.484 Γ— 10⁹⁹(100-digit number)
34849363722059339199…09696187906641551361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.969 Γ— 10⁹⁹(100-digit number)
69698727444118678399…19392375813283102721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.393 Γ— 10¹⁰⁰(101-digit number)
13939745488823735679…38784751626566205441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.787 Γ— 10¹⁰⁰(101-digit number)
27879490977647471359…77569503253132410881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.575 Γ— 10¹⁰⁰(101-digit number)
55758981955294942719…55139006506264821761
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 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
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 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 420524

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 4ebb9dc0d7155714eb2c09e63c409de37fceaf29f7023ace5c06ecb1e75d7155

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 #420,524 on Chainz β†—
Circulating Supply:57,848,654 XPMΒ·at block #6,825,568 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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