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Home/Chain Registry/Block #2,137,543

Block #2,137,543

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/30/2017, 3:29:07 AM Β· Difficulty 10.8875 Β· 4,706,300 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
9141e0c61b8e4f820e551c69068a21792cbc8dc9ac1974056a02b3dac85e50d2
View on Chainz β†—

Difficulty

10.887507

Transactions

1

Size

200 B

Version

2

Bits

0ae333a9

Nonce

2,069,103,064

Timestamp

5/30/2017, 3:29:07 AM

Confirmations

4,706,300

Merkle Root

d4b817ddd12523840dafb1b99f45128421fd00fbf63baec8a9383f9b1d86fc31
Transactions (1)
Coinbased4b817ddd12523…383f9b1d86fc31
1 in β†’ 1 out8.4200 XPM110 B
AcZ1PUNW…EQr3nTbq
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.

7.402 Γ— 10⁹³(94-digit number)
74020469950240934114…90958574037099284480
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
7.402 Γ— 10⁹³(94-digit number)
74020469950240934114…90958574037099284481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.480 Γ— 10⁹⁴(95-digit number)
14804093990048186822…81917148074198568961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.960 Γ— 10⁹⁴(95-digit number)
29608187980096373645…63834296148397137921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.921 Γ— 10⁹⁴(95-digit number)
59216375960192747291…27668592296794275841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.184 Γ— 10⁹⁡(96-digit number)
11843275192038549458…55337184593588551681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.368 Γ— 10⁹⁡(96-digit number)
23686550384077098916…10674369187177103361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.737 Γ— 10⁹⁡(96-digit number)
47373100768154197833…21348738374354206721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.474 Γ— 10⁹⁡(96-digit number)
94746201536308395666…42697476748708413441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.894 Γ— 10⁹⁢(97-digit number)
18949240307261679133…85394953497416826881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.789 Γ— 10⁹⁢(97-digit number)
37898480614523358266…70789906994833653761
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 2137543

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 9141e0c61b8e4f820e551c69068a21792cbc8dc9ac1974056a02b3dac85e50d2

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 #2,137,543 on Chainz β†—
Circulating Supply:57,995,110 XPMΒ·at block #6,843,842 Β· updates every 60s
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