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Home/Chain Registry/Block #221,579

Block #221,579

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/21/2013, 3:50:32 PM Β· Difficulty 9.9393 Β· 6,573,046 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3a786535405b2f68b1202c17fb0c28450077018c1e667fb8ebb00d98c24ea0b4
View on Chainz β†—

Height

#221,579

Difficulty

9.939280

Transactions

1

Size

208 B

Version

2

Bits

09f074aa

Nonce

5,180

Timestamp

10/21/2013, 3:50:32 PM

Confirmations

6,573,046

Merkle Root

86e2811ca9977fe2309b02e7851ed8f0a6c20871813ecf449c10c95ef21cb52d
Transactions (1)
Coinbase86e2811ca9977f…10c95ef21cb52d
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.

4.468 Γ— 10⁹⁸(99-digit number)
44681676602670878475…39547849121277359820
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
4.468 Γ— 10⁹⁸(99-digit number)
44681676602670878475…39547849121277359821
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.936 Γ— 10⁹⁸(99-digit number)
89363353205341756950…79095698242554719641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.787 Γ— 10⁹⁹(100-digit number)
17872670641068351390…58191396485109439281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.574 Γ— 10⁹⁹(100-digit number)
35745341282136702780…16382792970218878561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.149 Γ— 10⁹⁹(100-digit number)
71490682564273405560…32765585940437757121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.429 Γ— 10¹⁰⁰(101-digit number)
14298136512854681112…65531171880875514241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.859 Γ— 10¹⁰⁰(101-digit number)
28596273025709362224…31062343761751028481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.719 Γ— 10¹⁰⁰(101-digit number)
57192546051418724448…62124687523502056961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.143 Γ— 10¹⁰¹(102-digit number)
11438509210283744889…24249375047004113921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.287 Γ— 10¹⁰¹(102-digit number)
22877018420567489779…48498750094008227841
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 221579

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 3a786535405b2f68b1202c17fb0c28450077018c1e667fb8ebb00d98c24ea0b4

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 #221,579 on Chainz β†—
Circulating Supply:57,601,045 XPMΒ·at block #6,794,624 Β· updates every 60s
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