Block #168,965

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 9/17/2013, 4:15:29 PM · Difficulty 9.8684 · 6,620,867 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

37012aad087ee3e94c481cf547d04aa1c1f70cccb185a39308087aadab80e298

View on Chainz ↗

Height

#168,965

Difficulty

9.868358

Transactions

Size

424 B

Version

Bits

09de4cb3

Nonce

22,373

Timestamp

9/17/2013, 4:15:29 PM

Confirmations

6,620,867

Merkle Root

65914f45b02f5daad2c23b363a689edf02388877a979d944a80a956e907c9fde

Transactions (2)

Coinbase6da460ee9815f3…01237653829204

1 in → 1 out10.2600 XPM109 B

AZv7gMUK…CbiASjGW

ff44f3e8797fe2…33d74c72b6c6ff

1 in → 2 out2.2106 XPM226 B

AP4exjFF…2JJqgYei Abwxxahm…6C8gg5XP

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.

1.147 × 10⁹²(93-digit number)

11470956744377968714…16092803691077071359

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

1.147 × 10⁹²(93-digit number)

11470956744377968714…16092803691077071359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.294 × 10⁹²(93-digit number)

22941913488755937429…32185607382154142719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

4.588 × 10⁹²(93-digit number)

45883826977511874858…64371214764308285439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

9.176 × 10⁹²(93-digit number)

91767653955023749716…28742429528616570879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.835 × 10⁹³(94-digit number)

18353530791004749943…57484859057233141759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.670 × 10⁹³(94-digit number)

36707061582009499886…14969718114466283519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

7.341 × 10⁹³(94-digit number)

73414123164018999773…29939436228932567039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.468 × 10⁹⁴(95-digit number)

14682824632803799954…59878872457865134079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.936 × 10⁹⁴(95-digit number)

29365649265607599909…19757744915730268159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

5.873 × 10⁹⁴(95-digit number)

58731298531215199818…39515489831460536319

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