Block #315,985

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/16/2013, 7:46:26 PM · Difficulty 10.1202 · 6,480,929 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

ca883b2d4942da949b58a8b09aa0edcd08da2c78e91111e8100321c5fec203a5

View on Chainz ↗

Height

#315,985

Difficulty

10.120186

Transactions

Size

1.05 KB

Version

Bits

0a1ec47e

Nonce

5,105

Timestamp

12/16/2013, 7:46:26 PM

Confirmations

6,480,929

Mined by

⛏️ QaRX;AQwRN8bEjE7sawFBq7N38V9niAV8PsTcY9

Merkle Root

38fbff0ebe5b120d62a465d456995f4a26fde390b2c3b31a6806f44805655dfe

Transactions (1)

Coinbase38fbff0ebe5b12…06f44805655dfe

1 in → 27 out9.7500 XPM981 B

AQwRN8bE…V8PsTcY9 AYtDvcGs…VuAcA7m7 Aac9Hjdg…P4ktypc3 Ad9pSzHt…cpJ3y2zz Ac6mGvmQ…XqWmPHjR

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.

6.964 × 10⁹⁶(97-digit number)

69643336463033520266…68951215128520748161

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

6.964 × 10⁹⁶(97-digit number)

69643336463033520266…68951215128520748161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.392 × 10⁹⁷(98-digit number)

13928667292606704053…37902430257041496321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.785 × 10⁹⁷(98-digit number)

27857334585213408106…75804860514082992641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

5.571 × 10⁹⁷(98-digit number)

55714669170426816213…51609721028165985281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.114 × 10⁹⁸(99-digit number)

11142933834085363242…03219442056331970561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

2.228 × 10⁹⁸(99-digit number)

22285867668170726485…06438884112663941121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

4.457 × 10⁹⁸(99-digit number)

44571735336341452970…12877768225327882241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

8.914 × 10⁹⁸(99-digit number)

89143470672682905941…25755536450655764481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.782 × 10⁹⁹(100-digit number)

17828694134536581188…51511072901311528961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

3.565 × 10⁹⁹(100-digit number)

35657388269073162376…03022145802623057921

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