Block #75,088

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/21/2013, 2:34:20 PM · Difficulty 8.9959 · 6,714,956 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

a54278966f848fefac5f40ad599aa52f86eefcbbadeaa92c3fcf649d66dd8bc3

View on Chainz ↗

Height

#75,088

Difficulty

8.995904

Transactions

Size

199 B

Version

Bits

08fef38e

Nonce

357

Timestamp

7/21/2013, 2:34:20 PM

Confirmations

6,714,956

Merkle Root

ba35b8d7dbd542e6bbb824398bffba4cf2dfb253c9a585be5b00c9e7d472fc8b

Transactions (1)

Coinbaseba35b8d7dbd542…00c9e7d472fc8b

1 in → 1 out12.3400 XPM110 B

ARNQ5kND…tHzaRDhE

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.

6.713 × 10⁹¹(92-digit number)

67139130208190626031…71075641626837709179

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

6.713 × 10⁹¹(92-digit number)

67139130208190626031…71075641626837709179

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.342 × 10⁹²(93-digit number)

13427826041638125206…42151283253675418359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.685 × 10⁹²(93-digit number)

26855652083276250412…84302566507350836719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

5.371 × 10⁹²(93-digit number)

53711304166552500825…68605133014701673439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.074 × 10⁹³(94-digit number)

10742260833310500165…37210266029403346879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.148 × 10⁹³(94-digit number)

21484521666621000330…74420532058806693759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

4.296 × 10⁹³(94-digit number)

42969043333242000660…48841064117613387519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

8.593 × 10⁹³(94-digit number)

85938086666484001320…97682128235226775039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.718 × 10⁹⁴(95-digit number)

17187617333296800264…95364256470453550079

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 First 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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …

Cross-reference on Chainz Explorer