Block #363,464

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/17/2014, 10:41:44 AM · Difficulty 10.4135 · 6,446,984 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

8988e1e1621d6595d4767a44d100b5b899cba6221828c45d7427c433f6c1c4b6

View on Chainz ↗

Height

#363,464

Difficulty

10.413456

Transactions

Size

230 B

Version

Bits

0a69d846

Nonce

111,126

Timestamp

1/17/2014, 10:41:44 AM

Confirmations

6,446,984

Mined by

⛏️ P2SHARmAMwyuAi8euPwQcDptyGopF9P7Kn74ZT

Merkle Root

f2610a5a8e35061c04818978e7a983f697a171dcb5ceaeaf7e1db35575eadbcd

Transactions (1)

Coinbasef2610a5a8e3506…1db35575eadbcd

1 in → 2 out9.2100 XPM137 B

ARmAMwyu…P7Kn74ZT Abiw8n3q…ZnZfgvQW

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.

2.916 × 10¹⁰¹(102-digit number)

29160138924576040149…33120588957287075201

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

2.916 × 10¹⁰¹(102-digit number)

29160138924576040149…33120588957287075201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

5.832 × 10¹⁰¹(102-digit number)

58320277849152080298…66241177914574150401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.166 × 10¹⁰²(103-digit number)

11664055569830416059…32482355829148300801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.332 × 10¹⁰²(103-digit number)

23328111139660832119…64964711658296601601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

4.665 × 10¹⁰²(103-digit number)

46656222279321664238…29929423316593203201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

9.331 × 10¹⁰²(103-digit number)

93312444558643328477…59858846633186406401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.866 × 10¹⁰³(104-digit number)

18662488911728665695…19717693266372812801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

3.732 × 10¹⁰³(104-digit number)

37324977823457331391…39435386532745625601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

7.464 × 10¹⁰³(104-digit number)

74649955646914662782…78870773065491251201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.492 × 10¹⁰⁴(105-digit number)

14929991129382932556…57741546130982502401

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.

★★☆☆☆

Rarity

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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, …

Cross-reference on Chainz Explorer

Block #363,464

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