Block #75,634

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/21/2013, 5:46:58 PM · Difficulty 9.0250 · 6,720,945 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

67e48a80a21801a8d57c86c996318cc45d11a1ac18ed67637c97ea35676267d9

View on Chainz ↗

Height

#75,634

Difficulty

9.025008

Transactions

Size

577 B

Version

Bits

090666ee

Nonce

1,593

Timestamp

7/21/2013, 5:46:58 PM

Confirmations

6,720,945

Mined by

⛏️ P2SHAYzskyVn1s3Sv1VPwmjZuH7cWwtjpTqP12

Merkle Root

3bcf60993e6a62ed9b50024aaa4bcb655fdedc958f24bf2b9becee54658bb676

Transactions (2)

Coinbase1696e8efd29c42…cc9c21033d8589

1 in → 1 out12.2700 XPM110 B

AYzskyVn…tjpTqP12

8b51566cbc1c9d…f55e9cbb91e658

2 in → 2 out335.0600 XPM374 B

APE1dWFB…3PrGLeMk ATVGMzTK…dTGxc85J

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.

1.565 × 10¹⁰²(103-digit number)

15651395629167221056…77321890557787811681

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

1.565 × 10¹⁰²(103-digit number)

15651395629167221056…77321890557787811681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.130 × 10¹⁰²(103-digit number)

31302791258334442112…54643781115575623361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

6.260 × 10¹⁰²(103-digit number)

62605582516668884224…09287562231151246721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.252 × 10¹⁰³(104-digit number)

12521116503333776844…18575124462302493441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.504 × 10¹⁰³(104-digit number)

25042233006667553689…37150248924604986881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

5.008 × 10¹⁰³(104-digit number)

50084466013335107379…74300497849209973761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.001 × 10¹⁰⁴(105-digit number)

10016893202667021475…48600995698419947521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.003 × 10¹⁰⁴(105-digit number)

20033786405334042951…97201991396839895041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

4.006 × 10¹⁰⁴(105-digit number)

40067572810668085903…94403982793679790081

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