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Block #450,145

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/19/2014, 2:35:57 AM Β· Difficulty 10.3696 Β· 6,349,084 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e23881f02f3d732bda479e08e7a131670c3885e15fc1dce2d8edf318e665c488
View on Chainz β†—

Height

#450,145

Difficulty

10.369638

Transactions

1

Size

200 B

Version

2

Bits

0a5ea091

Nonce

12,394

Timestamp

3/19/2014, 2:35:57 AM

Confirmations

6,349,084

Merkle Root

615be4a523912d380465a7137bb4d447aed768696857a6de2c3fd3e6d06dc935
Transactions (1)
Coinbase615be4a523912d…3fd3e6d06dc935
1 in β†’ 1 out9.2900 XPM109 B
AabS6QUc…TMWaL7FZ
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.

1.666 Γ— 10⁹⁸(99-digit number)
16660593211826374269…05348178294739102720
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
1.666 Γ— 10⁹⁸(99-digit number)
16660593211826374269…05348178294739102719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.332 Γ— 10⁹⁸(99-digit number)
33321186423652748538…10696356589478205439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.664 Γ— 10⁹⁸(99-digit number)
66642372847305497077…21392713178956410879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.332 Γ— 10⁹⁹(100-digit number)
13328474569461099415…42785426357912821759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.665 Γ— 10⁹⁹(100-digit number)
26656949138922198831…85570852715825643519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.331 Γ— 10⁹⁹(100-digit number)
53313898277844397662…71141705431651287039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.066 Γ— 10¹⁰⁰(101-digit number)
10662779655568879532…42283410863302574079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.132 Γ— 10¹⁰⁰(101-digit number)
21325559311137759064…84566821726605148159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.265 Γ— 10¹⁰⁰(101-digit number)
42651118622275518129…69133643453210296319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.530 Γ— 10¹⁰⁰(101-digit number)
85302237244551036259…38267286906420592639
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 450145

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 e23881f02f3d732bda479e08e7a131670c3885e15fc1dce2d8edf318e665c488

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 #450,145 on Chainz β†—
Circulating Supply:57,637,875 XPMΒ·at block #6,799,228 Β· updates every 60s
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