Block #246,024

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 11/5/2013, 8:02:49 PM · Difficulty 9.9644 · 6,548,055 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

a7ef48d67a575cb23bf1a0aa6f6d396e237e7c25a5efdbc61d1a681989227057

View on Chainz ↗

Height

#246,024

Difficulty

9.964411

Transactions

Size

389 B

Version

Bits

09f6e39f

Nonce

21,450

Timestamp

11/5/2013, 8:02:49 PM

Confirmations

6,548,055

Merkle Root

64cbd5eb9c8430b12364617b450da3aa95af2f3820977d50668d4dbbecb8b323

Transactions (2)

Coinbase42a202f5a3ce5e…ebdd13b3273183

1 in → 1 out10.0700 XPM109 B

AG985Dnz…z3fiYGsJ

09b81fb99db817…e2747a074d3a96

1 in → 1 out117.6511 XPM192 B

APH3Qiac…89d34WiU

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.

7.224 × 10⁹⁰(91-digit number)

72242009539100912008…61795088673574427079

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

7.224 × 10⁹⁰(91-digit number)

72242009539100912008…61795088673574427079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.444 × 10⁹¹(92-digit number)

14448401907820182401…23590177347148854159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.889 × 10⁹¹(92-digit number)

28896803815640364803…47180354694297708319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

5.779 × 10⁹¹(92-digit number)

57793607631280729606…94360709388595416639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.155 × 10⁹²(93-digit number)

11558721526256145921…88721418777190833279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.311 × 10⁹²(93-digit number)

23117443052512291842…77442837554381666559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

4.623 × 10⁹²(93-digit number)

46234886105024583685…54885675108763333119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

9.246 × 10⁹²(93-digit number)

92469772210049167370…09771350217526666239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.849 × 10⁹³(94-digit number)

18493954442009833474…19542700435053332479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

3.698 × 10⁹³(94-digit number)

36987908884019666948…39085400870106664959

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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