XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,226,124

Block #2,226,124

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/28/2017, 2:39:08 AM Β· Difficulty 10.9478 Β· 4,616,200 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a1993c3a432d3d9cad4e14567fdc8213416066a1428e43db05f4a4e0643b46af
View on Chainz β†—

Difficulty

10.947820

Transactions

1

Size

200 B

Version

2

Bits

0af2a450

Nonce

625,392,751

Timestamp

7/28/2017, 2:39:08 AM

Confirmations

4,616,200

Merkle Root

54b26ad64e5c31f422dea9f2eea8212767c28289aa4d7a612a6baf74f99542bc
Transactions (1)
Coinbase54b26ad64e5c31…6baf74f99542bc
1 in β†’ 1 out8.3300 XPM110 B
AYxTvXaP…W6kepNNi
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.

2.522 Γ— 10⁹⁴(95-digit number)
25220348152261759401…81061143312148323720
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
2.522 Γ— 10⁹⁴(95-digit number)
25220348152261759401…81061143312148323721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.044 Γ— 10⁹⁴(95-digit number)
50440696304523518802…62122286624296647441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.008 Γ— 10⁹⁡(96-digit number)
10088139260904703760…24244573248593294881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.017 Γ— 10⁹⁡(96-digit number)
20176278521809407521…48489146497186589761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.035 Γ— 10⁹⁡(96-digit number)
40352557043618815042…96978292994373179521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.070 Γ— 10⁹⁡(96-digit number)
80705114087237630084…93956585988746359041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.614 Γ— 10⁹⁢(97-digit number)
16141022817447526016…87913171977492718081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.228 Γ— 10⁹⁢(97-digit number)
32282045634895052033…75826343954985436161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.456 Γ— 10⁹⁢(97-digit number)
64564091269790104067…51652687909970872321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.291 Γ— 10⁹⁷(98-digit number)
12912818253958020813…03305375819941744641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.582 Γ— 10⁹⁷(98-digit number)
25825636507916041626…06610751639883489281
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 2226124

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 a1993c3a432d3d9cad4e14567fdc8213416066a1428e43db05f4a4e0643b46af

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 #2,226,124 on Chainz β†—
Circulating Supply:57,982,999 XPMΒ·at block #6,842,323 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