Block #268,418

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 11/22/2013, 3:00:45 AM · Difficulty 9.9572 · 6,523,294 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

ee580cea69433a224091e6ee0f60940ce469ebbbfd454563f308b446cd2d701d

View on Chainz ↗

Height

#268,418

Difficulty

9.957195

Transactions

Size

1.08 KB

Version

Bits

09f50ab9

Nonce

49,563

Timestamp

11/22/2013, 3:00:45 AM

Confirmations

6,523,294

Merkle Root

d020bb448bf37b3d534d2983f9cf4fef26c0067daf94e6a87e7f61056bbc3a20

Transactions (4)

Coinbaseb2e7fdab5a4632…40ac7555d938af

1 in → 1 out10.1000 XPM109 B

AJPNi9av…PG3ZDZt4

a842e2a9b20e11…c46277873ccc2f

3 in → 2 out456.0102 XPM524 B

ATPM2yfs…AQmg5mid AXtSeECx…3q5ZfmWn

90489c70cc48f5…4138f1b0412c0b

1 in → 1 out10.1300 XPM158 B

AWD493jS…qaaun2vp

bf0a9a4a9f01db…8c379acecd8b71

1 in → 2 out9.9900 XPM225 B

AXovrw1N…MuWi69Hj AZAGtx3d…zGQTU9Z1

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.

1.498 × 10⁹³(94-digit number)

14983921080084497715…55056102769472772279

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

1.498 × 10⁹³(94-digit number)

14983921080084497715…55056102769472772279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.996 × 10⁹³(94-digit number)

29967842160168995431…10112205538945544559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

5.993 × 10⁹³(94-digit number)

59935684320337990862…20224411077891089119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.198 × 10⁹⁴(95-digit number)

11987136864067598172…40448822155782178239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.397 × 10⁹⁴(95-digit number)

23974273728135196344…80897644311564356479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

4.794 × 10⁹⁴(95-digit number)

47948547456270392689…61795288623128712959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

9.589 × 10⁹⁴(95-digit number)

95897094912540785379…23590577246257425919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.917 × 10⁹⁵(96-digit number)

19179418982508157075…47181154492514851839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.835 × 10⁹⁵(96-digit number)

38358837965016314151…94362308985029703679

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