Block #277,170

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/27/2013, 11:32:07 AM · Difficulty 9.9654 · 6,549,873 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

0988736d7a00b8bcf1cb6f3994f57ec208cb573f24653a3404130302c335c75d

View on Chainz ↗

Height

#277,170

Difficulty

9.965421

Transactions

Size

235 B

Version

Bits

09f725ce

Nonce

1,185

Timestamp

11/27/2013, 11:32:07 AM

Confirmations

6,549,873

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

afec51c9a18df941060e0c92eca951388c3b65bf20476396c156cbf2b0d80567

Transactions (1)

Coinbaseafec51c9a18df9…56cbf2b0d80567

1 in → 2 out10.0500 XPM142 B

AKcbk49N…GJbKa7j1 AU6kq4CL…dQBLvxLp

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.

7.490 × 10¹⁰²(103-digit number)

74908055849005854518…67542174362137018301

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

7.490 × 10¹⁰²(103-digit number)

74908055849005854518…67542174362137018301

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.498 × 10¹⁰³(104-digit number)

14981611169801170903…35084348724274036601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.996 × 10¹⁰³(104-digit number)

29963222339602341807…70168697448548073201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

5.992 × 10¹⁰³(104-digit number)

59926444679204683614…40337394897096146401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.198 × 10¹⁰⁴(105-digit number)

11985288935840936722…80674789794192292801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

2.397 × 10¹⁰⁴(105-digit number)

23970577871681873445…61349579588384585601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

4.794 × 10¹⁰⁴(105-digit number)

47941155743363746891…22699159176769171201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

9.588 × 10¹⁰⁴(105-digit number)

95882311486727493783…45398318353538342401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.917 × 10¹⁰⁵(106-digit number)

19176462297345498756…90796636707076684801

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 #277,170

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