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Block #226,420

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/25/2013, 5:17:04 AM Β· Difficulty 9.9360 Β· 6,585,700 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2544baedc1a6ef853bbdf3b6e4d99e73c565512effd1c04be26a0cad97cf7bcf
View on Chainz β†—

Height

#226,420

Difficulty

9.935987

Transactions

1

Size

207 B

Version

2

Bits

09ef9cd8

Nonce

4,407

Timestamp

10/25/2013, 5:17:04 AM

Confirmations

6,585,700

Merkle Root

a924144eb310bed87716e4a082505a9f4d1888c0bcb44768f9ca41564cfef713
Transactions (1)
Coinbasea924144eb310be…ca41564cfef713
1 in β†’ 1 out10.1100 XPM116 B
AcLBm5Z9…S683d7c3
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.

1.556 Γ— 10⁹⁸(99-digit number)
15563049676028875866…90591782271855618720
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
1.556 Γ— 10⁹⁸(99-digit number)
15563049676028875866…90591782271855618721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.112 Γ— 10⁹⁸(99-digit number)
31126099352057751733…81183564543711237441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.225 Γ— 10⁹⁸(99-digit number)
62252198704115503467…62367129087422474881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.245 Γ— 10⁹⁹(100-digit number)
12450439740823100693…24734258174844949761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.490 Γ— 10⁹⁹(100-digit number)
24900879481646201386…49468516349689899521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.980 Γ— 10⁹⁹(100-digit number)
49801758963292402773…98937032699379799041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.960 Γ— 10⁹⁹(100-digit number)
99603517926584805547…97874065398759598081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.992 Γ— 10¹⁰⁰(101-digit number)
19920703585316961109…95748130797519196161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.984 Γ— 10¹⁰⁰(101-digit number)
39841407170633922218…91496261595038392321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.968 Γ— 10¹⁰⁰(101-digit number)
79682814341267844437…82992523190076784641
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 226420

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 2544baedc1a6ef853bbdf3b6e4d99e73c565512effd1c04be26a0cad97cf7bcf

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 #226,420 on Chainz β†—
Circulating Supply:57,740,971 XPMΒ·at block #6,812,119 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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