Block #174,525

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 9/21/2013, 5:29:16 PM · Difficulty 9.8615 · 6,631,648 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

a87ac1842120c75d7e44e88ff2888ce60c20a994ba1c6ce012634831efa8e486

View on Chainz ↗

Height

#174,525

Difficulty

9.861465

Transactions

Size

683 B

Version

Bits

09dc88f5

Nonce

245,260

Timestamp

9/21/2013, 5:29:16 PM

Confirmations

6,631,648

Mined by

⛏️ P2SHAULd2vuSsxLZuDU7h1QVRmAJPSqrpbsLHm

Merkle Root

25c60a901f0eb3c9617a1254705e7f7f5b94cd46eed90b5bc47aeaa3d70292d9

Transactions (2)

Coinbasedca159833e088d…7c4a5182135dc1

1 in → 1 out10.2800 XPM109 B

AULd2vuS…qrpbsLHm

5295770d8f370e…686d2c60bb4915

3 in → 1 out364.9900 XPM487 B

AJADixXS…fSVYyLWJ

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.

1.446 × 10⁸⁸(89-digit number)

14467105733368910778…65510653161550549021

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

1.446 × 10⁸⁸(89-digit number)

14467105733368910778…65510653161550549021

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.893 × 10⁸⁸(89-digit number)

28934211466737821557…31021306323101098041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

5.786 × 10⁸⁸(89-digit number)

57868422933475643114…62042612646202196081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.157 × 10⁸⁹(90-digit number)

11573684586695128622…24085225292404392161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.314 × 10⁸⁹(90-digit number)

23147369173390257245…48170450584808784321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

4.629 × 10⁸⁹(90-digit number)

46294738346780514491…96340901169617568641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

9.258 × 10⁸⁹(90-digit number)

92589476693561028983…92681802339235137281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.851 × 10⁹⁰(91-digit number)

18517895338712205796…85363604678470274561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

3.703 × 10⁹⁰(91-digit number)

37035790677424411593…70727209356940549121

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 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

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 2CC formula:

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

Cross-reference on Chainz Explorer