Block #164,973

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 9/14/2013, 11:50:15 PM · Difficulty 9.8648 · 6,624,860 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

bac2c7f22d728fa6b3c878a7d7d44d54db3aebedfce4ae4280b47d2c95860ddb

View on Chainz ↗

Height

#164,973

Difficulty

9.864800

Transactions

Size

198 B

Version

Bits

09dd6390

Nonce

15,940

Timestamp

9/14/2013, 11:50:15 PM

Confirmations

6,624,860

Merkle Root

07ee8a0201bbd4eed8ed626b36b46de28ccb455d0344866219a38424710ccbcd

Transactions (1)

Coinbase07ee8a0201bbd4…a38424710ccbcd

1 in → 1 out10.2600 XPM109 B

AZv7gMUK…CbiASjGW

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.

9.711 × 10⁹²(93-digit number)

97119550344628211621…84099092520133528671

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

9.711 × 10⁹²(93-digit number)

97119550344628211621…84099092520133528671

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.942 × 10⁹³(94-digit number)

19423910068925642324…68198185040267057341

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

3.884 × 10⁹³(94-digit number)

38847820137851284648…36396370080534114681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

7.769 × 10⁹³(94-digit number)

77695640275702569297…72792740161068229361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.553 × 10⁹⁴(95-digit number)

15539128055140513859…45585480322136458721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

3.107 × 10⁹⁴(95-digit number)

31078256110281027718…91170960644272917441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

6.215 × 10⁹⁴(95-digit number)

62156512220562055437…82341921288545834881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.243 × 10⁹⁵(96-digit number)

12431302444112411087…64683842577091669761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.486 × 10⁹⁵(96-digit number)

24862604888224822175…29367685154183339521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

4.972 × 10⁹⁵(96-digit number)

49725209776449644350…58735370308366679041

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