Block #69,793

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/20/2013, 10:29:50 AM · Difficulty 8.9914 · 6,740,616 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

6965c19989fac5a5a6196834aad42063c53b872406e9fe97c5b7897779ed69a1

View on Chainz ↗

Height

#69,793

Difficulty

8.991383

Transactions

Size

198 B

Version

Bits

08fdcb47

Nonce

Timestamp

7/20/2013, 10:29:50 AM

Confirmations

6,740,616

Mined by

⛏️ P2SHAJbRF9Vh3Pm1qDnFdVGkh4jvYocmDMZyVK

Merkle Root

60f390f0f1dc407bc7e8190b9f681b7ec3fd012dae5f85b35f0cd2e02c9caec2

Transactions (1)

Coinbase60f390f0f1dc40…0cd2e02c9caec2

1 in → 1 out12.3500 XPM110 B

AJbRF9Vh…cmDMZyVK

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.

1.070 × 10⁸⁹(90-digit number)

10700545018553115211…39054952243422933499

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

1.070 × 10⁸⁹(90-digit number)

10700545018553115211…39054952243422933499

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.140 × 10⁸⁹(90-digit number)

21401090037106230423…78109904486845866999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

4.280 × 10⁸⁹(90-digit number)

42802180074212460846…56219808973691733999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

8.560 × 10⁸⁹(90-digit number)

85604360148424921693…12439617947383467999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.712 × 10⁹⁰(91-digit number)

17120872029684984338…24879235894766935999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.424 × 10⁹⁰(91-digit number)

34241744059369968677…49758471789533871999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

6.848 × 10⁹⁰(91-digit number)

68483488118739937354…99516943579067743999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.369 × 10⁹¹(92-digit number)

13696697623747987470…99033887158135487999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.739 × 10⁹¹(92-digit number)

27393395247495974941…98067774316270975999

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

Block #69,793

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