XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #480,726

Block #480,726

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/8/2014, 11:38:35 AM Β· Difficulty 10.5214 Β· 6,317,176 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4c6626ee1b53f8589a30536ac8706967e493726eebfc649140f726c5ab2b3da7
View on Chainz β†—

Height

#480,726

Difficulty

10.521394

Transactions

1

Size

199 B

Version

2

Bits

0a857a10

Nonce

148,998

Timestamp

4/8/2014, 11:38:35 AM

Confirmations

6,317,176

Merkle Root

a744ed7dc619c94cfdeb248621ff0f547cf54a4cd37a9a3539d079de0788c7e0
Transactions (1)
Coinbasea744ed7dc619c9…d079de0788c7e0
1 in β†’ 1 out9.0200 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.

1.798 Γ— 10⁹³(94-digit number)
17980239030163170175…13202352291041820640
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
1.798 Γ— 10⁹³(94-digit number)
17980239030163170175…13202352291041820641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.596 Γ— 10⁹³(94-digit number)
35960478060326340351…26404704582083641281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.192 Γ— 10⁹³(94-digit number)
71920956120652680702…52809409164167282561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.438 Γ— 10⁹⁴(95-digit number)
14384191224130536140…05618818328334565121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.876 Γ— 10⁹⁴(95-digit number)
28768382448261072280…11237636656669130241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.753 Γ— 10⁹⁴(95-digit number)
57536764896522144561…22475273313338260481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.150 Γ— 10⁹⁡(96-digit number)
11507352979304428912…44950546626676520961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.301 Γ— 10⁹⁡(96-digit number)
23014705958608857824…89901093253353041921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.602 Γ— 10⁹⁡(96-digit number)
46029411917217715649…79802186506706083841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
9.205 Γ— 10⁹⁡(96-digit number)
92058823834435431298…59604373013412167681
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 480726

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 4c6626ee1b53f8589a30536ac8706967e493726eebfc649140f726c5ab2b3da7

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 #480,726 on Chainz β†—
Circulating Supply:57,627,208 XPMΒ·at block #6,797,901 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK