Home/Chain Registry/Block #435,976

Block #435,976

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/9/2014, 7:26:52 AM · Difficulty 10.3551 · 6,389,594 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

4fea0f3f80569ca00eec93455663db823f69f0e34eb113e91e0ebf2e5f4df9d5

View on Chainz ↗

Height

#435,976

Difficulty

10.355079

Transactions

Size

1.51 KB

Version

Bits

0a5ae67b

Nonce

39,514

Timestamp

3/9/2014, 7:26:52 AM

Confirmations

6,389,594

Merkle Root

382c5bac51a11d7afb95e19723b459da673738db09829ffbf2647dcd1ac764e3

Transactions (4)

Coinbase834a94a0d39d0f…4687e0e8ce1e40

1 in → 21 out9.3400 XPM777 B

AGz9gyZW…bo8NYQpw AdFLJFhb…bsaVkAyh AVRMvm7T…6PC6keBx AUzEPJFG…kYkA5U9V ATp4jJhs…TbSgR8Qb

7051334b590665…b79212814992b6

1 in → 2 out4.1479 XPM226 B

ATyqYN6j…nmtysCgb AG2LtRh6…LEzx7suz

e442563338aadb…1fc4d4c28d7212

1 in → 2 out3.6162 XPM225 B

AMqJoTsB…BkNufxCh AdpsxmtJ…ZWfmvRK9

fb247f5e82adf1…df272f8a7f8f62

1 in → 2 out0.5823 XPM227 B

AKYe7Ebo…jA1tjzHr AcxbARPG…d6kxmukV

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.

3.414 × 10⁹⁰(91-digit number)

34149237463329273431…75080813858456448000

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

3.414 × 10⁹⁰(91-digit number)

34149237463329273431…75080813858456448001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

6.829 × 10⁹⁰(91-digit number)

68298474926658546863…50161627716912896001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.365 × 10⁹¹(92-digit number)

13659694985331709372…00323255433825792001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.731 × 10⁹¹(92-digit number)

27319389970663418745…00646510867651584001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

5.463 × 10⁹¹(92-digit number)

54638779941326837490…01293021735303168001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.092 × 10⁹²(93-digit number)

10927755988265367498…02586043470606336001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.185 × 10⁹²(93-digit number)

21855511976530734996…05172086941212672001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

4.371 × 10⁹²(93-digit number)

43711023953061469992…10344173882425344001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

8.742 × 10⁹²(93-digit number)

87422047906122939984…20688347764850688001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.748 × 10⁹³(94-digit number)

17484409581224587996…41376695529701376001

Verify on FactorDB ↗Wolfram Alpha ↗

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 — 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

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 × 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 435976

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 4fea0f3f80569ca00eec93455663db823f69f0e34eb113e91e0ebf2e5f4df9d5

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 #435,976 on Chainz ↗

Block #435,976

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