Block #88,076

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/29/2013, 8:37:02 AM · Difficulty 9.2732 · 6,707,347 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

a75b2e2a4a87ef6fa5a75a4d45c6ee53da2086e53d0fb7d3f93fa1d39e557ebc

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Height

#88,076

Difficulty

9.273190

Transactions

Size

1.79 KB

Version

Bits

0945efc8

Nonce

19,354

Timestamp

7/29/2013, 8:37:02 AM

Confirmations

6,707,347

Mined by

⛏️ P2SHAXLw2aRPYYPFFpsV5yWkbuXFjuXXd4m397

Merkle Root

96064ad6464526d4baf25c6d339b654ffefa4319443ebf6c5e1d13004836cc14

Transactions (3)

Coinbase89a25568b50970…45d68da8f88d04

1 in → 1 out11.6400 XPM109 B

AXLw2aRP…XXd4m397

47220034a33db2…520b6330fa9f00

9 in → 2 out102.5635 XPM1.38 KB

AHUgkEqf…b9YEDMVk AeGRXBWR…faHrRNNt

bf648761312d11…93ccaf8deae413

1 in → 2 out11.5900 XPM225 B

AVmyV7mf…x5k36296 AH6tDGYV…Hfei4zWZ

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.

5.539 × 10¹⁰²(103-digit number)

55390015625343180468…21230420943483849799

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

5.539 × 10¹⁰²(103-digit number)

55390015625343180468…21230420943483849799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.107 × 10¹⁰³(104-digit number)

11078003125068636093…42460841886967699599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.215 × 10¹⁰³(104-digit number)

22156006250137272187…84921683773935399199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

4.431 × 10¹⁰³(104-digit number)

44312012500274544374…69843367547870798399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

8.862 × 10¹⁰³(104-digit number)

88624025000549088749…39686735095741596799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.772 × 10¹⁰⁴(105-digit number)

17724805000109817749…79373470191483193599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

3.544 × 10¹⁰⁴(105-digit number)

35449610000219635499…58746940382966387199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

7.089 × 10¹⁰⁴(105-digit number)

70899220000439270999…17493880765932774399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.417 × 10¹⁰⁵(106-digit number)

14179844000087854199…34987761531865548799

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