Block #299,794

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 12/8/2013, 5:09:24 AM · Difficulty 9.9921 · 6,499,229 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

a273dd3ce1bf704c443e36f29410a2b0f1c5aea5dba05e8cad82f951fd9d1f5b

View on Chainz ↗

Height

#299,794

Difficulty

9.992147

Transactions

Size

1.13 KB

Version

Bits

09fdfd5e

Nonce

115,297

Timestamp

12/8/2013, 5:09:24 AM

Confirmations

6,499,229

Mined by

⛏️ aRAdCkmCQcQHVCyw3ZifSd7QridiL4UdmY7c

Merkle Root

657f7a34de85026181deb56e82886336b66e838d049dff3541e76d73575c527f

Transactions (2)

Coinbase1a033def773cd5…94d00764fcbb72

1 in → 23 out10.0000 XPM845 B

AdCkmCQc…L4UdmY7c APeshfYV…3PKcKMKH Ad9pSzHt…cpJ3y2zz AQyr8Lw3…hs4nt3Pn ASWX42VM…XypQABkY

4c382395a03828…ddd4a2a92b985b

1 in → 2 out30.7003 XPM225 B

AcNMcQjS…CHQDFpjE AJdvJmjS…GFTusQmv

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.

2.305 × 10⁸⁸(89-digit number)

23052984223537551796…64956487759930553999

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

2.305 × 10⁸⁸(89-digit number)

23052984223537551796…64956487759930553999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

4.610 × 10⁸⁸(89-digit number)

46105968447075103592…29912975519861107999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

9.221 × 10⁸⁸(89-digit number)

92211936894150207184…59825951039722215999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.844 × 10⁸⁹(90-digit number)

18442387378830041436…19651902079444431999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

3.688 × 10⁸⁹(90-digit number)

36884774757660082873…39303804158888863999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

7.376 × 10⁸⁹(90-digit number)

73769549515320165747…78607608317777727999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.475 × 10⁹⁰(91-digit number)

14753909903064033149…57215216635555455999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.950 × 10⁹⁰(91-digit number)

29507819806128066299…14430433271110911999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

5.901 × 10⁹⁰(91-digit number)

59015639612256132598…28860866542221823999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.180 × 10⁹¹(92-digit number)

11803127922451226519…57721733084443647999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^10 × origin − 1

2.360 × 10⁹¹(92-digit number)

23606255844902453039…15443466168887295999

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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