XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,470,262

Block #2,470,262

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/13/2018, 12:44:49 AM Β· Difficulty 10.9609 Β· 4,373,567 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
64fcda2927b303a22446ebc8749f4dfe7c7a29f198b08f3296d8b99b8d9e8396
View on Chainz β†—

Difficulty

10.960865

Transactions

1

Size

201 B

Version

2

Bits

0af5fb38

Nonce

191,712,464

Timestamp

1/13/2018, 12:44:49 AM

Confirmations

4,373,567

Merkle Root

ebd0ffd9bc2911764d7d2f55d8e7690fa1f14a217b3cbc23b7012802b27356cb
Transactions (1)
Coinbaseebd0ffd9bc2911…012802b27356cb
1 in β†’ 1 out8.3100 XPM110 B
AT12MH5L…9oRtyaBS
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.

2.068 Γ— 10⁹⁢(97-digit number)
20681873395683783716…05587367082949236480
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
2.068 Γ— 10⁹⁢(97-digit number)
20681873395683783716…05587367082949236481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.136 Γ— 10⁹⁢(97-digit number)
41363746791367567432…11174734165898472961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.272 Γ— 10⁹⁢(97-digit number)
82727493582735134864…22349468331796945921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.654 Γ— 10⁹⁷(98-digit number)
16545498716547026972…44698936663593891841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.309 Γ— 10⁹⁷(98-digit number)
33090997433094053945…89397873327187783681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.618 Γ— 10⁹⁷(98-digit number)
66181994866188107891…78795746654375567361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.323 Γ— 10⁹⁸(99-digit number)
13236398973237621578…57591493308751134721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.647 Γ— 10⁹⁸(99-digit number)
26472797946475243156…15182986617502269441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.294 Γ— 10⁹⁸(99-digit number)
52945595892950486313…30365973235004538881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.058 Γ— 10⁹⁹(100-digit number)
10589119178590097262…60731946470009077761
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 2470262

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 64fcda2927b303a22446ebc8749f4dfe7c7a29f198b08f3296d8b99b8d9e8396

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 #2,470,262 on Chainz β†—
Circulating Supply:57,995,008 XPMΒ·at block #6,843,828 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.
Privacy PolicyΒ·
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

Β·Privacy Policy