Block #72,288

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/20/2013, 11:15:56 PM · Difficulty 8.9939 · 6,718,720 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

de2422b078e956e46be1a3cecfec8050e316c84b0db6dba032f523955e1a2c4f

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Height

#72,288

Difficulty

8.993948

Transactions

Size

203 B

Version

Bits

08fe7366

Nonce

450

Timestamp

7/20/2013, 11:15:56 PM

Confirmations

6,718,720

Merkle Root

2a62f495403d72970089c6c37a3551dce27331a23d2da6508a4a2f4f30879a80

Transactions (1)

Coinbase2a62f495403d72…4a2f4f30879a80

1 in → 1 out12.3400 XPM110 B

AJGWp62K…d7vtT3BW

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.

6.565 × 10¹⁰¹(102-digit number)

65655153469887049673…75878698999752651861

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

6.565 × 10¹⁰¹(102-digit number)

65655153469887049673…75878698999752651861

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.313 × 10¹⁰²(103-digit number)

13131030693977409934…51757397999505303721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.626 × 10¹⁰²(103-digit number)

26262061387954819869…03514795999010607441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

5.252 × 10¹⁰²(103-digit number)

52524122775909639738…07029591998021214881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.050 × 10¹⁰³(104-digit number)

10504824555181927947…14059183996042429761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

2.100 × 10¹⁰³(104-digit number)

21009649110363855895…28118367992084859521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

4.201 × 10¹⁰³(104-digit number)

42019298220727711790…56236735984169719041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

8.403 × 10¹⁰³(104-digit number)

84038596441455423581…12473471968339438081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.680 × 10¹⁰⁴(105-digit number)

16807719288291084716…24946943936678876161

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