Block #76,382

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/22/2013, 12:05:21 AM · Difficulty 9.0943 · 6,715,036 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

8638ba3980dbf6dedf0d3aee995f8cdd3aacc9c2528e4a4bc08966be7c335408

View on Chainz ↗

Height

#76,382

Difficulty

9.094312

Transactions

Size

2.22 KB

Version

Bits

091824cf

Nonce

565

Timestamp

7/22/2013, 12:05:21 AM

Confirmations

6,715,036

Merkle Root

852c296f281dbf70bb7b2258ef3132f3849ce0a4b052b02086016d7bf6725fcf

Transactions (3)

Coinbasea5bed7fffdeb29…ea31b9e758d3a8

1 in → 1 out12.1000 XPM110 B

ARP4gFr4…BH7GStru

1a3570e5bb9744…fca5f1127809ed

16 in → 2 out197.4400 XPM1.86 KB

AavPgC8q…QkeeSVBs AZiCNyEn…BjhGoBch

4c53b8cfcead8c…d052ac64fb1c3e

1 in → 1 out12.3300 XPM158 B

AZoJpc2e…kz2E4KZR

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.

1.527 × 10¹⁰¹(102-digit number)

15278729689092461962…62185699143384581001

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

1.527 × 10¹⁰¹(102-digit number)

15278729689092461962…62185699143384581001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.055 × 10¹⁰¹(102-digit number)

30557459378184923924…24371398286769162001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

6.111 × 10¹⁰¹(102-digit number)

61114918756369847849…48742796573538324001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.222 × 10¹⁰²(103-digit number)

12222983751273969569…97485593147076648001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.444 × 10¹⁰²(103-digit number)

24445967502547939139…94971186294153296001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

4.889 × 10¹⁰²(103-digit number)

48891935005095878279…89942372588306592001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

9.778 × 10¹⁰²(103-digit number)

97783870010191756558…79884745176613184001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.955 × 10¹⁰³(104-digit number)

19556774002038351311…59769490353226368001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

3.911 × 10¹⁰³(104-digit number)

39113548004076702623…19538980706452736001

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