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Block #449,030

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/18/2014, 8:25:47 AM Β· Difficulty 10.3663 Β· 6,351,672 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
042fe2b5d578be273eaf83d4bdba9b8f3977e1bfff409378eb2cc585a52d6d8b
View on Chainz β†—

Height

#449,030

Difficulty

10.366280

Transactions

1

Size

200 B

Version

2

Bits

0a5dc485

Nonce

148,103

Timestamp

3/18/2014, 8:25:47 AM

Confirmations

6,351,672

Merkle Root

dc443805589d697093151a976ff80da9ccbac8f32ed8771d78eaaf2da5115873
Transactions (1)
Coinbasedc443805589d69…eaaf2da5115873
1 in β†’ 1 out9.2900 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.

1.337 Γ— 10⁹⁡(96-digit number)
13376031292332163267…38050944295446070400
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
1.337 Γ— 10⁹⁡(96-digit number)
13376031292332163267…38050944295446070399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.675 Γ— 10⁹⁡(96-digit number)
26752062584664326535…76101888590892140799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.350 Γ— 10⁹⁡(96-digit number)
53504125169328653070…52203777181784281599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.070 Γ— 10⁹⁢(97-digit number)
10700825033865730614…04407554363568563199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.140 Γ— 10⁹⁢(97-digit number)
21401650067731461228…08815108727137126399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.280 Γ— 10⁹⁢(97-digit number)
42803300135462922456…17630217454274252799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.560 Γ— 10⁹⁢(97-digit number)
85606600270925844913…35260434908548505599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.712 Γ— 10⁹⁷(98-digit number)
17121320054185168982…70520869817097011199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.424 Γ— 10⁹⁷(98-digit number)
34242640108370337965…41041739634194022399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.848 Γ— 10⁹⁷(98-digit number)
68485280216740675930…82083479268388044799
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 449030

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 042fe2b5d578be273eaf83d4bdba9b8f3977e1bfff409378eb2cc585a52d6d8b

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 #449,030 on Chainz β†—
Circulating Supply:57,649,682 XPMΒ·at block #6,800,701 Β· updates every 60s
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