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Block #22,139

2CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/12/2013, 4:29:37 PM Β· Difficulty 7.9498 Β· 6,794,120 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4999ae49967eda2e3dd9bdb343421ad5bbb5ba6cd4d2f8ee71ab735ef2992233
View on Chainz β†—

Height

#22,139

Difficulty

7.949837

Transactions

1

Size

197 B

Version

2

Bits

07f32887

Nonce

978

Timestamp

7/12/2013, 4:29:37 PM

Confirmations

6,794,120

Merkle Root

17d746953c55a301038a437e4a20b73f1a49fb1b88676320cf484b1195b57dd1
Transactions (1)
Coinbase17d746953c55a3…484b1195b57dd1
1 in β†’ 1 out15.8000 XPM108 B
AMURGbeq…HNpQDxEA
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.

2.286 Γ— 10⁹³(94-digit number)
22860902758741090739…97939693991503601250
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
2.286 Γ— 10⁹³(94-digit number)
22860902758741090739…97939693991503601251
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.572 Γ— 10⁹³(94-digit number)
45721805517482181479…95879387983007202501
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.144 Γ— 10⁹³(94-digit number)
91443611034964362959…91758775966014405001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.828 Γ— 10⁹⁴(95-digit number)
18288722206992872591…83517551932028810001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.657 Γ— 10⁹⁴(95-digit number)
36577444413985745183…67035103864057620001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.315 Γ— 10⁹⁴(95-digit number)
73154888827971490367…34070207728115240001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.463 Γ— 10⁹⁡(96-digit number)
14630977765594298073…68140415456230480001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.926 Γ— 10⁹⁡(96-digit number)
29261955531188596147…36280830912460960001
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 22139

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 4999ae49967eda2e3dd9bdb343421ad5bbb5ba6cd4d2f8ee71ab735ef2992233

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 #22,139 on Chainz β†—
Circulating Supply:57,774,193 XPMΒ·at block #6,816,258 Β· updates every 60s
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