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Block #22,019

2CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/12/2013, 4:11:44 PM Β· Difficulty 7.9488 Β· 6,792,136 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4a38ff3f799b2e8980e3098eeec8b155be701312dc150ae85fce0a3db2e573ff
View on Chainz β†—

Height

#22,019

Difficulty

7.948805

Transactions

1

Size

194 B

Version

2

Bits

07f2e4dc

Nonce

61

Timestamp

7/12/2013, 4:11:44 PM

Confirmations

6,792,136

Merkle Root

83a2495d58316986342bd915232ea70a7c9db1270a6ee590f385ff310de674df
Transactions (1)
Coinbase83a2495d583169…85ff310de674df
1 in β†’ 1 out15.8100 XPM108 B
ASKRZHR1…j7AFn1ro
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.

2.088 Γ— 10⁸⁴(85-digit number)
20884179571166992993…46283072918973192800
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
2.088 Γ— 10⁸⁴(85-digit number)
20884179571166992993…46283072918973192801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.176 Γ— 10⁸⁴(85-digit number)
41768359142333985987…92566145837946385601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.353 Γ— 10⁸⁴(85-digit number)
83536718284667971975…85132291675892771201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.670 Γ— 10⁸⁡(86-digit number)
16707343656933594395…70264583351785542401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.341 Γ— 10⁸⁡(86-digit number)
33414687313867188790…40529166703571084801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.682 Γ— 10⁸⁡(86-digit number)
66829374627734377580…81058333407142169601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.336 Γ— 10⁸⁢(87-digit number)
13365874925546875516…62116666814284339201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.673 Γ— 10⁸⁢(87-digit number)
26731749851093751032…24233333628568678401
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 8 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 8
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 22019

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 4a38ff3f799b2e8980e3098eeec8b155be701312dc150ae85fce0a3db2e573ff

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 #22,019 on Chainz β†—
Circulating Supply:57,757,319 XPMΒ·at block #6,814,154 Β· updates every 60s
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