Block #269,863

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 11/23/2013, 12:49:08 PM · Difficulty 9.9520 · 6,521,583 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

30e68b41625081466796774a3848ae7c17ae5a6ec3c4592b1045348c9a658836

View on Chainz ↗

Height

#269,863

Difficulty

9.952011

Transactions

Size

1.29 KB

Version

Bits

09f3b706

Nonce

535,909

Timestamp

11/23/2013, 12:49:08 PM

Confirmations

6,521,583

Merkle Root

cd812705486c4592818fd11251b689c877d3f85e76465a57a2e2d3930310a674

Transactions (4)

Coinbasea00db1c36da514…a9bf4e642356d9

1 in → 1 out10.1100 XPM109 B

AFp6FK3d…ihVNjJTs

319b8a5cda2705…6c716957b69aeb

4 in → 2 out478.8530 XPM669 B

AV1XaCWZ…2ZTgHVdW ALTaBWLf…n2W1djq6

af8835240d2335…e6322193d9a682

1 in → 2 out279.9900 XPM225 B

ATaAgzUw…dFaowiWQ AY4H42CP…4bQ4ZA3H

2ad971fffd95f8…61222cf9aeceaa

1 in → 2 out299.9900 XPM227 B

ARUJZqpK…wLzyWNGN AaYZWXSz…FAC24iNx

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.

4.234 × 10⁹³(94-digit number)

42340946427744483295…62212906800765016959

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

4.234 × 10⁹³(94-digit number)

42340946427744483295…62212906800765016959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

8.468 × 10⁹³(94-digit number)

84681892855488966590…24425813601530033919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.693 × 10⁹⁴(95-digit number)

16936378571097793318…48851627203060067839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

3.387 × 10⁹⁴(95-digit number)

33872757142195586636…97703254406120135679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

6.774 × 10⁹⁴(95-digit number)

67745514284391173272…95406508812240271359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.354 × 10⁹⁵(96-digit number)

13549102856878234654…90813017624480542719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.709 × 10⁹⁵(96-digit number)

27098205713756469308…81626035248961085439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

5.419 × 10⁹⁵(96-digit number)

54196411427512938617…63252070497922170879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.083 × 10⁹⁶(97-digit number)

10839282285502587723…26504140995844341759

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