Home/Chain Registry/Block #2,643,931

Block #2,643,931

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 5/2/2018, 7:08:29 AM · Difficulty 11.6974 · 4,188,138 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

e84b816fb2588b923ae34abbecbe1b8783768809357d8ae488a5062c2db20bb1

View on Chainz ↗

Height

#2,643,931

Difficulty

11.697449

Transactions

Size

846 B

Version

Bits

0bb28c08

Nonce

218,199,787

Timestamp

5/2/2018, 7:08:29 AM

Confirmations

4,188,138

Merkle Root

d23fa186d8bb16f50be53daa97f89d0087f0cf42f88fe088e7b8a039554b4c4c

Transactions (4)

Coinbase2e01f93e1e6c70…dbf095ea9a9ddd

1 in → 1 out7.3300 XPM110 B

AadhrhtV…ii4Bu1bq

5592ca2c4da419…7965f5ba349539

1 in → 2 out7.4200 XPM191 B

AVMbBt3B…S6tHzQNQ AXU2VgsN…RePZXTgf

2452c3b53e1847…77fef15e60964e

1 in → 2 out2.3404 XPM227 B

AS3tNJHb…CYPNJYSb ARJTFmXi…9mT6237k

ce5b2903363b43…db7d48b78a4644

1 in → 2 out1.3526 XPM227 B

AdfBDFBy…UX3ZpkZr AJN1ao9K…CUKW4qu3

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.309 × 10⁹⁷(98-digit number)

23095798565738740227…25019561238370631680

Discovered Prime Numbers

p_k = 2^k × 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.

origin + 1

2.309 × 10⁹⁷(98-digit number)

23095798565738740227…25019561238370631681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

4.619 × 10⁹⁷(98-digit number)

46191597131477480454…50039122476741263361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

9.238 × 10⁹⁷(98-digit number)

92383194262954960908…00078244953482526721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.847 × 10⁹⁸(99-digit number)

18476638852590992181…00156489906965053441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

3.695 × 10⁹⁸(99-digit number)

36953277705181984363…00312979813930106881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

7.390 × 10⁹⁸(99-digit number)

73906555410363968726…00625959627860213761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.478 × 10⁹⁹(100-digit number)

14781311082072793745…01251919255720427521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.956 × 10⁹⁹(100-digit number)

29562622164145587490…02503838511440855041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

5.912 × 10⁹⁹(100-digit number)

59125244328291174981…05007677022881710081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.182 × 10¹⁰⁰(101-digit number)

11825048865658234996…10015354045763420161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^10 × origin + 1

2.365 × 10¹⁰⁰(101-digit number)

23650097731316469992…20030708091526840321

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Cunningham Chain of the Second Kind. The prime chain origin — the large number shown above — 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 →

★★★☆☆

Rarity

RareChain length 11

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 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 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 2643931

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 e84b816fb2588b923ae34abbecbe1b8783768809357d8ae488a5062c2db20bb1

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 → Debug Window → 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 #2,643,931 on Chainz ↗

Block #2,643,931

Cookie Preferences