XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #22,627

Block #22,627

2CCLength 7β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/12/2013, 5:48:08 PM Β· Difficulty 7.9538 Β· 6,777,989 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
873703d0302358f213740ede613bbafe2d58f98c4cc48b351dec7382449d97bb
View on Chainz β†—

Height

#22,627

Difficulty

7.953764

Transactions

1

Size

203 B

Version

2

Bits

07f429de

Nonce

93

Timestamp

7/12/2013, 5:48:08 PM

Confirmations

6,777,989

Merkle Root

af297065fd0b9bfb888d8a3beb798b8fb134bf2816e816025aeecd43acc5e639
Transactions (1)
Coinbaseaf297065fd0b9b…eecd43acc5e639
1 in β†’ 1 out15.7900 XPM108 B
AYTtnr7Z…AUx4dVQg
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.

2.534 Γ— 10¹⁰⁢(107-digit number)
25347789288929396172…27205349773327296800
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
2.534 Γ— 10¹⁰⁢(107-digit number)
25347789288929396172…27205349773327296801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.069 Γ— 10¹⁰⁢(107-digit number)
50695578577858792344…54410699546654593601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.013 Γ— 10¹⁰⁷(108-digit number)
10139115715571758468…08821399093309187201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.027 Γ— 10¹⁰⁷(108-digit number)
20278231431143516937…17642798186618374401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.055 Γ— 10¹⁰⁷(108-digit number)
40556462862287033875…35285596373236748801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.111 Γ— 10¹⁰⁷(108-digit number)
81112925724574067751…70571192746473497601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.622 Γ— 10¹⁰⁸(109-digit number)
16222585144914813550…41142385492946995201
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 7 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 7
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 22627

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 873703d0302358f213740ede613bbafe2d58f98c4cc48b351dec7382449d97bb

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 #22,627 on Chainz β†—
Circulating Supply:57,648,990 XPMΒ·at block #6,800,615 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