XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #227,376

Block #227,376

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/25/2013, 8:14:43 PM Β· Difficulty 9.9367 Β· 6,579,020 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2ad752f975a72a5dfe8087b352201021d00ee99c3a80b6d65defe4e3f50e132a
View on Chainz β†—

Height

#227,376

Difficulty

9.936705

Transactions

1

Size

199 B

Version

2

Bits

09efcbe1

Nonce

325,510

Timestamp

10/25/2013, 8:14:43 PM

Confirmations

6,579,020

Merkle Root

ec5f98d7add2b5703ed1612875a80f64bf2e1af2e8c54fc9b4938b936f61c4ca
Transactions (1)
Coinbaseec5f98d7add2b5…938b936f61c4ca
1 in β†’ 1 out10.1100 XPM109 B
ASj3o7xf…p4aXP1Vn
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.

6.815 Γ— 10⁹³(94-digit number)
68153307117686754869…90729772162271080960
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
6.815 Γ— 10⁹³(94-digit number)
68153307117686754869…90729772162271080961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.363 Γ— 10⁹⁴(95-digit number)
13630661423537350973…81459544324542161921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.726 Γ— 10⁹⁴(95-digit number)
27261322847074701947…62919088649084323841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.452 Γ— 10⁹⁴(95-digit number)
54522645694149403895…25838177298168647681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.090 Γ— 10⁹⁡(96-digit number)
10904529138829880779…51676354596337295361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.180 Γ— 10⁹⁡(96-digit number)
21809058277659761558…03352709192674590721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.361 Γ— 10⁹⁡(96-digit number)
43618116555319523116…06705418385349181441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.723 Γ— 10⁹⁡(96-digit number)
87236233110639046233…13410836770698362881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.744 Γ— 10⁹⁢(97-digit number)
17447246622127809246…26821673541396725761
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 227376

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 2ad752f975a72a5dfe8087b352201021d00ee99c3a80b6d65defe4e3f50e132a

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 #227,376 on Chainz β†—
Circulating Supply:57,695,260 XPMΒ·at block #6,806,395 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

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