Block #94,360

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 8/3/2013, 1:16:51 AM · Difficulty 9.2020 · 6,720,102 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

64370f5bfbff880a5a84e28ae2512554bd941f6ccd2d897593fcaa29ac7bc7fe

View on Chainz ↗

Height

#94,360

Difficulty

9.202018

Transactions

Size

4.48 KB

Version

Bits

0933b76e

Nonce

20,699

Timestamp

8/3/2013, 1:16:51 AM

Confirmations

6,720,102

Mined by

⛏️ P2SHAL45pFjGak5LH5k31wYjx3AdJARsi7xB2x

Merkle Root

d489e57623cb9a7bc242449b7917e311d1d98abd063a360708532ccf24e9d3f3

Transactions (2)

Coinbase90909fc112cb6a…dd86ec4c2427e9

1 in → 1 out11.8400 XPM109 B

AL45pFjG…Rsi7xB2x

f1cee39b3e7b8f…a74f123e9f410f

38 in → 1 out500.0000 XPM4.28 KB

AdD9gugr…dxcSMAJi

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.

8.360 × 10¹¹⁰(111-digit number)

83608870174844475709…99633086589560033599

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

8.360 × 10¹¹⁰(111-digit number)

83608870174844475709…99633086589560033599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.672 × 10¹¹¹(112-digit number)

16721774034968895141…99266173179120067199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.344 × 10¹¹¹(112-digit number)

33443548069937790283…98532346358240134399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

6.688 × 10¹¹¹(112-digit number)

66887096139875580567…97064692716480268799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.337 × 10¹¹²(113-digit number)

13377419227975116113…94129385432960537599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.675 × 10¹¹²(113-digit number)

26754838455950232227…88258770865921075199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

5.350 × 10¹¹²(113-digit number)

53509676911900464454…76517541731842150399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.070 × 10¹¹³(114-digit number)

10701935382380092890…53035083463684300799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.140 × 10¹¹³(114-digit number)

21403870764760185781…06070166927368601599

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 #94,360

Cookie Preferences