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Block #432,387

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/6/2014, 8:53:20 PM Β· Difficulty 10.3428 Β· 6,362,164 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
afa2da6238f2b81eefdabbdc4a77f7539d45262bc4ec99c46acd549bc773a4c0
View on Chainz β†—

Height

#432,387

Difficulty

10.342777

Transactions

1

Size

200 B

Version

2

Bits

0a57c036

Nonce

7,480

Timestamp

3/6/2014, 8:53:20 PM

Confirmations

6,362,164

Merkle Root

79f63e1b98787c588e343fa3673af500f1a22247b30b20990053ecba79595e75
Transactions (1)
Coinbase79f63e1b98787c…53ecba79595e75
1 in β†’ 1 out9.3300 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.

6.737 Γ— 10⁹⁡(96-digit number)
67374133906981299788…53001038423204172480
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
6.737 Γ— 10⁹⁡(96-digit number)
67374133906981299788…53001038423204172479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.347 Γ— 10⁹⁢(97-digit number)
13474826781396259957…06002076846408344959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.694 Γ— 10⁹⁢(97-digit number)
26949653562792519915…12004153692816689919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.389 Γ— 10⁹⁢(97-digit number)
53899307125585039830…24008307385633379839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.077 Γ— 10⁹⁷(98-digit number)
10779861425117007966…48016614771266759679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.155 Γ— 10⁹⁷(98-digit number)
21559722850234015932…96033229542533519359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.311 Γ— 10⁹⁷(98-digit number)
43119445700468031864…92066459085067038719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.623 Γ— 10⁹⁷(98-digit number)
86238891400936063728…84132918170134077439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.724 Γ— 10⁹⁸(99-digit number)
17247778280187212745…68265836340268154879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.449 Γ— 10⁹⁸(99-digit number)
34495556560374425491…36531672680536309759
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 432387

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 afa2da6238f2b81eefdabbdc4a77f7539d45262bc4ec99c46acd549bc773a4c0

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 #432,387 on Chainz β†—
Circulating Supply:57,600,449 XPMΒ·at block #6,794,550 Β· updates every 60s
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