Home/Chain Registry/Block #36,433

Block #36,433

2CCLength 7★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/14/2013, 9:23:48 AM · Difficulty 7.9954 · 6,753,309 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

7f7fb70dffcaaae9c8c8e99101c562993b62bd2e681b08d49ba66a8db1abb847

View on Chainz ↗

Height

#36,433

Difficulty

7.995372

Transactions

Size

199 B

Version

Bits

07fed0b2

Nonce

394

Timestamp

7/14/2013, 9:23:48 AM

Confirmations

6,753,309

Merkle Root

fd218feef8b460d615f36279819bccf76d784bad766dae504b435f77ce6c59d7

Transactions (1)

Coinbasefd218feef8b460…435f77ce6c59d7

1 in → 1 out15.6200 XPM109 B

APwLyEjs…3A1KVWZd

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.

1.004 × 10⁹⁵(96-digit number)

10040104773310370042…90536351868272624640

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

1.004 × 10⁹⁵(96-digit number)

10040104773310370042…90536351868272624641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.008 × 10⁹⁵(96-digit number)

20080209546620740084…81072703736545249281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

4.016 × 10⁹⁵(96-digit number)

40160419093241480168…62145407473090498561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

8.032 × 10⁹⁵(96-digit number)

80320838186482960337…24290814946180997121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.606 × 10⁹⁶(97-digit number)

16064167637296592067…48581629892361994241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

3.212 × 10⁹⁶(97-digit number)

32128335274593184135…97163259784723988481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

6.425 × 10⁹⁶(97-digit number)

64256670549186368270…94326519569447976961

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 7 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

CommonChain length 7

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 36433

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 7f7fb70dffcaaae9c8c8e99101c562993b62bd2e681b08d49ba66a8db1abb847

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 #36,433 on Chainz ↗