Block #89,076

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/30/2013, 2:46:47 AM · Difficulty 9.2602 · 6,708,738 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

d9697895eb351abb4d0c476da079f78d2d4a6b497c91951f931cdb17fd8510bd

View on Chainz ↗

Height

#89,076

Difficulty

9.260199

Transactions

Size

2.03 KB

Version

Bits

09429c6b

Nonce

18,063

Timestamp

7/30/2013, 2:46:47 AM

Confirmations

6,708,738

Mined by

⛏️ P2SHAR4SMisi5YzFuV2tU86pVcjoRYPRa6dEfu

Merkle Root

fc1b769ecacffeb3db4c405d1b79591eebb03d11a0c5cfce689a887e3f82c8fe

Transactions (2)

Coinbasefa091b2df11ae4…409ebd42212fd2

1 in → 1 out11.6600 XPM109 B

AR4SMisi…PRa6dEfu

8f2c4914eef4b3…d0c0459fbc34d1

16 in → 1 out199.0000 XPM1.82 KB

AWqrmbWo…ZcSjTJTw

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.

6.854 × 10¹²⁰(121-digit number)

68542823711722176809…88680338851941080479

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

6.854 × 10¹²⁰(121-digit number)

68542823711722176809…88680338851941080479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.370 × 10¹²¹(122-digit number)

13708564742344435361…77360677703882160959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.741 × 10¹²¹(122-digit number)

27417129484688870723…54721355407764321919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

5.483 × 10¹²¹(122-digit number)

54834258969377741447…09442710815528643839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.096 × 10¹²²(123-digit number)

10966851793875548289…18885421631057287679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.193 × 10¹²²(123-digit number)

21933703587751096578…37770843262114575359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

4.386 × 10¹²²(123-digit number)

43867407175502193157…75541686524229150719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

8.773 × 10¹²²(123-digit number)

87734814351004386315…51083373048458301439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.754 × 10¹²³(124-digit number)

17546962870200877263…02166746096916602879

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