Block #61,431

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/18/2013, 1:23:51 PM · Difficulty 8.9731 · 6,748,687 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

19a9fbdd5845b825858eb8a95806c845aaa884f023a8d2676d3eae65e5151fe6

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Height

#61,431

Difficulty

8.973063

Transactions

Size

204 B

Version

Bits

08f91aa7

Nonce

563

Timestamp

7/18/2013, 1:23:51 PM

Confirmations

6,748,687

Mined by

⛏️ P2SHAXY6feytV6ZxBQJFLAbLwdMRw9oghmWWGf

Merkle Root

8cd4076d01e94e853d3ddcb54ef4ad1a0114f99f0d671d40f5ef6edaa89125cb

Transactions (1)

Coinbase8cd4076d01e94e…ef6edaa89125cb

1 in → 1 out12.4000 XPM110 B

AXY6feyt…oghmWWGf

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.

4.006 × 10¹⁰³(104-digit number)

40061574502998102448…56691416716969976441

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

4.006 × 10¹⁰³(104-digit number)

40061574502998102448…56691416716969976441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

8.012 × 10¹⁰³(104-digit number)

80123149005996204896…13382833433939952881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.602 × 10¹⁰⁴(105-digit number)

16024629801199240979…26765666867879905761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

3.204 × 10¹⁰⁴(105-digit number)

32049259602398481958…53531333735759811521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

6.409 × 10¹⁰⁴(105-digit number)

64098519204796963917…07062667471519623041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.281 × 10¹⁰⁵(106-digit number)

12819703840959392783…14125334943039246081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.563 × 10¹⁰⁵(106-digit number)

25639407681918785566…28250669886078492161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

5.127 × 10¹⁰⁵(106-digit number)

51278815363837571133…56501339772156984321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.025 × 10¹⁰⁶(107-digit number)

10255763072767514226…13002679544313968641

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #61,431

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