Block #79,806

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/23/2013, 6:06:48 PM · Difficulty 9.2433 · 6,709,964 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

c34b315fcc62dc939184647177b6cb80d8616f316f7c41544399de22f0138f70

View on Chainz ↗

Height

#79,806

Difficulty

9.243262

Transactions

Size

580 B

Version

Bits

093e466d

Nonce

Timestamp

7/23/2013, 6:06:48 PM

Confirmations

6,709,964

Merkle Root

51ae754e2ea04320bf1afb1eb9eff30ddbd40b3334593c4d27a5bb6f20f93d8e

Transactions (2)

Coinbase1cdf706a498d63…cf4cd11f834ee8

1 in → 1 out11.7000 XPM110 B

Ae9pHXPL…wqSw2nYL

ade2e196f77098…aac953fd7ba45f

2 in → 2 out439.1259 XPM375 B

ATk7bHnG…Xb8euRQv ANtegTSv…hzJnCaMa

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.

1.932 × 10¹⁰⁷(108-digit number)

19329792160839258257…12378683093338706491

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

1.932 × 10¹⁰⁷(108-digit number)

19329792160839258257…12378683093338706491

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.865 × 10¹⁰⁷(108-digit number)

38659584321678516515…24757366186677412981

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

7.731 × 10¹⁰⁷(108-digit number)

77319168643357033030…49514732373354825961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.546 × 10¹⁰⁸(109-digit number)

15463833728671406606…99029464746709651921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

3.092 × 10¹⁰⁸(109-digit number)

30927667457342813212…98058929493419303841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

6.185 × 10¹⁰⁸(109-digit number)

61855334914685626424…96117858986838607681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.237 × 10¹⁰⁹(110-digit number)

12371066982937125284…92235717973677215361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.474 × 10¹⁰⁹(110-digit number)

24742133965874250569…84471435947354430721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

4.948 × 10¹⁰⁹(110-digit number)

49484267931748501139…68942871894708861441

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