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Block #444,686

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/15/2014, 10:05:32 AM Β· Difficulty 10.3490 Β· 6,356,705 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
9f53fd4dc13950da95250349e6f338aae56c2b2b32b3959bcf8ea358ebc013cc
View on Chainz β†—

Height

#444,686

Difficulty

10.349048

Transactions

1

Size

202 B

Version

2

Bits

0a595b35

Nonce

197,912

Timestamp

3/15/2014, 10:05:32 AM

Confirmations

6,356,705

Merkle Root

e69b57478eafcfe4c803e375b595ccdf0368c5fea839da49f9ef3183c9ea3be9
Transactions (1)
Coinbasee69b57478eafcf…ef3183c9ea3be9
1 in β†’ 1 out9.3200 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.

4.395 Γ— 10⁹⁸(99-digit number)
43954108193106880084…56183143027976765440
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
4.395 Γ— 10⁹⁸(99-digit number)
43954108193106880084…56183143027976765441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.790 Γ— 10⁹⁸(99-digit number)
87908216386213760168…12366286055953530881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.758 Γ— 10⁹⁹(100-digit number)
17581643277242752033…24732572111907061761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.516 Γ— 10⁹⁹(100-digit number)
35163286554485504067…49465144223814123521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.032 Γ— 10⁹⁹(100-digit number)
70326573108971008134…98930288447628247041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.406 Γ— 10¹⁰⁰(101-digit number)
14065314621794201626…97860576895256494081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.813 Γ— 10¹⁰⁰(101-digit number)
28130629243588403253…95721153790512988161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.626 Γ— 10¹⁰⁰(101-digit number)
56261258487176806507…91442307581025976321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.125 Γ— 10¹⁰¹(102-digit number)
11252251697435361301…82884615162051952641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.250 Γ— 10¹⁰¹(102-digit number)
22504503394870722603…65769230324103905281
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 444686

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 9f53fd4dc13950da95250349e6f338aae56c2b2b32b3959bcf8ea358ebc013cc

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 #444,686 on Chainz β†—
Circulating Supply:57,655,194 XPMΒ·at block #6,801,390 Β· updates every 60s
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