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Home/Chain Registry/Block #1,182,043

Block #1,182,043

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/4/2015, 12:16:17 AM Β· Difficulty 10.9158 Β· 5,618,171 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
cc0991f45ba3d19d025a66e5aa20b7ba61e18d05e5c80262f74b99fae537b588
View on Chainz β†—

Difficulty

10.915833

Transactions

2

Size

424 B

Version

2

Bits

0aea740a

Nonce

234,094,863

Timestamp

8/4/2015, 12:16:17 AM

Confirmations

5,618,171

Merkle Root

feec10fbed17387e183a0e6c256955ad545a6a71c4109319454d5ad89994fff0
Transactions (2)
Coinbasec25ccc1e3f7cab…ff2f64ea47fb03
1 in β†’ 1 out8.3900 XPM109 B
AMe1eEUe…sFPN8Rdb
e69fedef2915e7…776614696a2c9b
1 in β†’ 2 out6.2877 XPM225 B
AcuM7XiJ…5uND8JceAMQw1LAB…hHxVksoo
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.

8.594 Γ— 10⁹⁴(95-digit number)
85944324700343757212…41154152315143640320
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
8.594 Γ— 10⁹⁴(95-digit number)
85944324700343757212…41154152315143640321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.718 Γ— 10⁹⁡(96-digit number)
17188864940068751442…82308304630287280641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.437 Γ— 10⁹⁡(96-digit number)
34377729880137502885…64616609260574561281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.875 Γ— 10⁹⁡(96-digit number)
68755459760275005770…29233218521149122561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.375 Γ— 10⁹⁢(97-digit number)
13751091952055001154…58466437042298245121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.750 Γ— 10⁹⁢(97-digit number)
27502183904110002308…16932874084596490241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.500 Γ— 10⁹⁢(97-digit number)
55004367808220004616…33865748169192980481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.100 Γ— 10⁹⁷(98-digit number)
11000873561644000923…67731496338385960961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.200 Γ— 10⁹⁷(98-digit number)
22001747123288001846…35462992676771921921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.400 Γ— 10⁹⁷(98-digit number)
44003494246576003692…70925985353543843841
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 1182043

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 cc0991f45ba3d19d025a66e5aa20b7ba61e18d05e5c80262f74b99fae537b588

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 #1,182,043 on Chainz β†—
Circulating Supply:57,645,762 XPMΒ·at block #6,800,213 Β· updates every 60s
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