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Home/Chain Registry/Block #2,133,329

Block #2,133,329

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/26/2017, 10:41:50 AM Β· Difficulty 10.9097 Β· 4,708,908 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
306ebb0acda4860da49563c3cd3482405b9d1fa10863f840d74f302540f93abd
View on Chainz β†—

Difficulty

10.909670

Transactions

1

Size

200 B

Version

2

Bits

0ae8e028

Nonce

429,989,229

Timestamp

5/26/2017, 10:41:50 AM

Confirmations

4,708,908

Merkle Root

6b74d61dfd87f3aeb377e44994bc21ad50768a2a44ae26ffab860ee325d421e6
Transactions (1)
Coinbase6b74d61dfd87f3…860ee325d421e6
1 in β†’ 1 out8.3900 XPM109 B
AadiT8EP…69khcZPF
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.

5.311 Γ— 10⁹⁢(97-digit number)
53115251998744667538…11242000484895744000
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
5.311 Γ— 10⁹⁢(97-digit number)
53115251998744667538…11242000484895744001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.062 Γ— 10⁹⁷(98-digit number)
10623050399748933507…22484000969791488001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.124 Γ— 10⁹⁷(98-digit number)
21246100799497867015…44968001939582976001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.249 Γ— 10⁹⁷(98-digit number)
42492201598995734031…89936003879165952001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.498 Γ— 10⁹⁷(98-digit number)
84984403197991468062…79872007758331904001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.699 Γ— 10⁹⁸(99-digit number)
16996880639598293612…59744015516663808001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.399 Γ— 10⁹⁸(99-digit number)
33993761279196587224…19488031033327616001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.798 Γ— 10⁹⁸(99-digit number)
67987522558393174449…38976062066655232001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.359 Γ— 10⁹⁹(100-digit number)
13597504511678634889…77952124133310464001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.719 Γ— 10⁹⁹(100-digit number)
27195009023357269779…55904248266620928001
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 2133329

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 306ebb0acda4860da49563c3cd3482405b9d1fa10863f840d74f302540f93abd

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 #2,133,329 on Chainz β†—
Circulating Supply:57,982,295 XPMΒ·at block #6,842,236 Β· updates every 60s
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