Home/Chain Registry/Block #375,633

Block #375,633

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/25/2014, 8:30:39 PM · Difficulty 10.4247 · 6,450,693 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

74147a4d5411cc07359ffca9d002f20e804f79e9d813ee77a72ff5fd97e0d5eb

View on Chainz ↗

Height

#375,633

Difficulty

10.424716

Transactions

Size

401 B

Version

Bits

0a6cba31

Nonce

24,376

Timestamp

1/25/2014, 8:30:39 PM

Confirmations

6,450,693

Merkle Root

db1b5d75f14f38fb757cff2192e05ba1676285b9578b990268f74d2fef25a1f8

Transactions (2)

Coinbaseb17d49c202f383…5824fb92980f73

1 in → 1 out9.2000 XPM116 B

AbwWkWZt…kawDhufa

7829ebddd48e5f…93b89ffc7eda51

1 in → 1 out0.9967 XPM192 B

AYLMhMP5…yNosfqe9

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.

3.028 × 10¹⁰²(103-digit number)

30286150273419921991…29562212193465794560

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

3.028 × 10¹⁰²(103-digit number)

30286150273419921991…29562212193465794561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

6.057 × 10¹⁰²(103-digit number)

60572300546839843982…59124424386931589121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.211 × 10¹⁰³(104-digit number)

12114460109367968796…18248848773863178241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.422 × 10¹⁰³(104-digit number)

24228920218735937593…36497697547726356481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

4.845 × 10¹⁰³(104-digit number)

48457840437471875186…72995395095452712961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

9.691 × 10¹⁰³(104-digit number)

96915680874943750372…45990790190905425921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.938 × 10¹⁰⁴(105-digit number)

19383136174988750074…91981580381810851841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

3.876 × 10¹⁰⁴(105-digit number)

38766272349977500148…83963160763621703681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

7.753 × 10¹⁰⁴(105-digit number)

77532544699955000297…67926321527243407361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.550 × 10¹⁰⁵(106-digit number)

15506508939991000059…35852643054486814721

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 375633

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 74147a4d5411cc07359ffca9d002f20e804f79e9d813ee77a72ff5fd97e0d5eb

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 #375,633 on Chainz ↗

Block #375,633

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