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Home/Chain Registry/Block #432,795

Block #432,795

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/7/2014, 4:08:24 AM Β· Difficulty 10.3390 Β· 6,394,459 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f05884f4aa619f22992c84d97d34bca37456d13f1e3de89eaeb7e914cacbb2ba
View on Chainz β†—

Height

#432,795

Difficulty

10.339014

Transactions

1

Size

200 B

Version

2

Bits

0a56c99c

Nonce

101,852

Timestamp

3/7/2014, 4:08:24 AM

Confirmations

6,394,459

Merkle Root

46d764fd2335c19d120963517626b2483b9645c28ea966c48e2dabc640188cd9
Transactions (1)
Coinbase46d764fd2335c1…2dabc640188cd9
1 in β†’ 1 out9.3400 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.

1.315 Γ— 10⁹⁡(96-digit number)
13154021141438481076…37047706724854860800
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
1.315 Γ— 10⁹⁡(96-digit number)
13154021141438481076…37047706724854860799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.630 Γ— 10⁹⁡(96-digit number)
26308042282876962153…74095413449709721599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.261 Γ— 10⁹⁡(96-digit number)
52616084565753924307…48190826899419443199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.052 Γ— 10⁹⁢(97-digit number)
10523216913150784861…96381653798838886399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.104 Γ— 10⁹⁢(97-digit number)
21046433826301569722…92763307597677772799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.209 Γ— 10⁹⁢(97-digit number)
42092867652603139445…85526615195355545599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.418 Γ— 10⁹⁢(97-digit number)
84185735305206278891…71053230390711091199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.683 Γ— 10⁹⁷(98-digit number)
16837147061041255778…42106460781422182399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.367 Γ— 10⁹⁷(98-digit number)
33674294122082511556…84212921562844364799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.734 Γ— 10⁹⁷(98-digit number)
67348588244165023113…68425843125688729599
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 432795

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 f05884f4aa619f22992c84d97d34bca37456d13f1e3de89eaeb7e914cacbb2ba

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 #432,795 on Chainz β†—
Circulating Supply:57,862,135 XPMΒ·at block #6,827,253 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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