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Block #460,004

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/25/2014, 4:42:57 PM Β· Difficulty 10.4213 Β· 6,356,092 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
30a3aa21748a71fca2fec1fae718e86e3cfc19d2718a2d041334b77ceaf6f303
View on Chainz β†—

Height

#460,004

Difficulty

10.421269

Transactions

2

Size

391 B

Version

2

Bits

0a6bd850

Nonce

65,483

Timestamp

3/25/2014, 4:42:57 PM

Confirmations

6,356,092

Merkle Root

e0379de0b1b0640667f8baaf8b9a61c60dafb489a95804953624a1539e202b40
Transactions (2)
Coinbase1b71bec4b002ed…c316c2365c93bb
1 in β†’ 1 out9.2000 XPM109 B
AGjPkStC…zy6gVDAd
7396353007a721…ed45b9a12ab884
1 in β†’ 1 out5.9927 XPM192 B
ARiaPuk5…UqHJYYuk
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.

6.408 Γ— 10⁹⁴(95-digit number)
64080457996157777126…81675992189762062400
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
6.408 Γ— 10⁹⁴(95-digit number)
64080457996157777126…81675992189762062399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.281 Γ— 10⁹⁡(96-digit number)
12816091599231555425…63351984379524124799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.563 Γ— 10⁹⁡(96-digit number)
25632183198463110850…26703968759048249599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.126 Γ— 10⁹⁡(96-digit number)
51264366396926221700…53407937518096499199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.025 Γ— 10⁹⁢(97-digit number)
10252873279385244340…06815875036192998399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.050 Γ— 10⁹⁢(97-digit number)
20505746558770488680…13631750072385996799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.101 Γ— 10⁹⁢(97-digit number)
41011493117540977360…27263500144771993599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.202 Γ— 10⁹⁢(97-digit number)
82022986235081954721…54527000289543987199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.640 Γ— 10⁹⁷(98-digit number)
16404597247016390944…09054000579087974399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.280 Γ— 10⁹⁷(98-digit number)
32809194494032781888…18108001158175948799
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 460004

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 30a3aa21748a71fca2fec1fae718e86e3cfc19d2718a2d041334b77ceaf6f303

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 #460,004 on Chainz β†—
Circulating Supply:57,772,889 XPMΒ·at block #6,816,095 Β· updates every 60s
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