Block #293,977

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/4/2013, 3:06:02 PM · Difficulty 9.9908 · 6,510,839 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

ae0baa4a26224e74c5f804382aa361a20aac642b1801bf81d9d094557a3b6672

View on Chainz ↗

Height

#293,977

Difficulty

9.990836

Transactions

Size

1.01 KB

Version

Bits

09fda775

Nonce

125

Timestamp

12/4/2013, 3:06:02 PM

Confirmations

6,510,839

Mined by

⛏️ Y|aRDAFqKfjezAQpHxUWGcDetimH5AUqX9Ace3g

Merkle Root

23c1dd6618fc613bfc4d35e4b8ec969f278f53319a1e127e07a0625f98843c64

Transactions (1)

Coinbase23c1dd6618fc61…a0625f98843c64

1 in → 26 out10.0000 XPM947 B

AFqKfjez…qX9Ace3g AXsfu4E3…ZifoNcUa AWXYBWKP…qQAoisBJ Ad9pSzHt…cpJ3y2zz AY4LyZBe…7DTvswxY

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.

2.589 × 10⁹⁵(96-digit number)

25894973134170100799…51547418395086544641

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

2.589 × 10⁹⁵(96-digit number)

25894973134170100799…51547418395086544641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

5.178 × 10⁹⁵(96-digit number)

51789946268340201599…03094836790173089281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.035 × 10⁹⁶(97-digit number)

10357989253668040319…06189673580346178561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.071 × 10⁹⁶(97-digit number)

20715978507336080639…12379347160692357121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

4.143 × 10⁹⁶(97-digit number)

41431957014672161279…24758694321384714241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

8.286 × 10⁹⁶(97-digit number)

82863914029344322559…49517388642769428481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.657 × 10⁹⁷(98-digit number)

16572782805868864511…99034777285538856961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

3.314 × 10⁹⁷(98-digit number)

33145565611737729023…98069554571077713921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

6.629 × 10⁹⁷(98-digit number)

66291131223475458047…96139109142155427841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.325 × 10⁹⁸(99-digit number)

13258226244695091609…92278218284310855681

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 Second 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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …

Cross-reference on Chainz Explorer