XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #524,258

Block #524,258

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/4/2014, 2:01:12 AM Β· Difficulty 10.8755 Β· 6,276,256 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d0c928948d7e8113b97c9d59119cdae1b7aedcb39a4b536ec347f0fa99740ef3
View on Chainz β†—

Height

#524,258

Difficulty

10.875481

Transactions

1

Size

200 B

Version

2

Bits

0ae01f86

Nonce

302,487

Timestamp

5/4/2014, 2:01:12 AM

Confirmations

6,276,256

Merkle Root

0c4cb2fa94f0c4aecea617b203bc63dc183bda16c76328693b3939094827cdda
Transactions (1)
Coinbase0c4cb2fa94f0c4…3939094827cdda
1 in β†’ 1 out8.4400 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.

2.433 Γ— 10⁹⁴(95-digit number)
24338524865091072390…81965848254946675000
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
2.433 Γ— 10⁹⁴(95-digit number)
24338524865091072390…81965848254946675001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.867 Γ— 10⁹⁴(95-digit number)
48677049730182144781…63931696509893350001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.735 Γ— 10⁹⁴(95-digit number)
97354099460364289562…27863393019786700001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.947 Γ— 10⁹⁡(96-digit number)
19470819892072857912…55726786039573400001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.894 Γ— 10⁹⁡(96-digit number)
38941639784145715825…11453572079146800001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.788 Γ— 10⁹⁡(96-digit number)
77883279568291431650…22907144158293600001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.557 Γ— 10⁹⁢(97-digit number)
15576655913658286330…45814288316587200001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.115 Γ— 10⁹⁢(97-digit number)
31153311827316572660…91628576633174400001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.230 Γ— 10⁹⁢(97-digit number)
62306623654633145320…83257153266348800001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.246 Γ— 10⁹⁷(98-digit number)
12461324730926629064…66514306532697600001
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 524258

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 d0c928948d7e8113b97c9d59119cdae1b7aedcb39a4b536ec347f0fa99740ef3

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 #524,258 on Chainz β†—
Circulating Supply:57,648,178 XPMΒ·at block #6,800,513 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