Block #78,331

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 7/22/2013, 7:04:03 PM · Difficulty 9.2291 · 6,746,484 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

0b9e091403bd5b8e74d5fbcf179d511f956db3fdebf145217b86cfaa55ec7af9

View on Chainz ↗

Height

#78,331

Difficulty

9.229119

Transactions

Size

203 B

Version

Bits

093aa792

Nonce

468

Timestamp

7/22/2013, 7:04:03 PM

Confirmations

6,746,484

Mined by

⛏️ P2SHAK774hxcgqrRkXMJuZuaucvipNDsMcBR7Z

Merkle Root

ab7739dc43c5d2f9ede4bb851af618b26c3106646f91755583e5361b74400f14

Transactions (1)

Coinbaseab7739dc43c5d2…e5361b74400f14

1 in → 1 out11.7200 XPM110 B

AK774hxc…DsMcBR7Z

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.

4.819 × 10¹⁰¹(102-digit number)

48197757219712921631…02562707467353628289

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

4.819 × 10¹⁰¹(102-digit number)

48197757219712921631…02562707467353628289

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

9.639 × 10¹⁰¹(102-digit number)

96395514439425843263…05125414934707256579

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.927 × 10¹⁰²(103-digit number)

19279102887885168652…10250829869414513159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

3.855 × 10¹⁰²(103-digit number)

38558205775770337305…20501659738829026319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

7.711 × 10¹⁰²(103-digit number)

77116411551540674610…41003319477658052639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.542 × 10¹⁰³(104-digit number)

15423282310308134922…82006638955316105279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

3.084 × 10¹⁰³(104-digit number)

30846564620616269844…64013277910632210559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

6.169 × 10¹⁰³(104-digit number)

61693129241232539688…28026555821264421119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.233 × 10¹⁰⁴(105-digit number)

12338625848246507937…56053111642528842239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

2.467 × 10¹⁰⁴(105-digit number)

24677251696493015875…12106223285057684479

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #78,331

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