Block #172,137

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 9/20/2013, 12:20:13 AM · Difficulty 9.8636 · 6,619,617 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

dbd5c38520ba9a48c96d512e6c70a53915a2bff47975021facc3ff6290333459

View on Chainz ↗

Height

#172,137

Difficulty

9.863551

Transactions

Size

426 B

Version

Bits

09dd11b3

Nonce

53,639

Timestamp

9/20/2013, 12:20:13 AM

Confirmations

6,619,617

Merkle Root

d8822ed3262940c49835731c5a25da9e9df46137e804a3e2371bbca7e95d82e0

Transactions (2)

Coinbaseef06d7810be946…4703483d3aa02d

1 in → 1 out10.2700 XPM109 B

AVdLj7zM…KMe4mftr

361485daa7fceb…ac9912b3cbf1d6

1 in → 2 out30.0322 XPM226 B

AY4uM53e…yee8uDKH AYhAdxUd…91nEwNUW

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.

2.708 × 10⁹⁷(98-digit number)

27087786976044814928…85914599322250444801

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

2.708 × 10⁹⁷(98-digit number)

27087786976044814928…85914599322250444801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

5.417 × 10⁹⁷(98-digit number)

54175573952089629856…71829198644500889601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.083 × 10⁹⁸(99-digit number)

10835114790417925971…43658397289001779201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.167 × 10⁹⁸(99-digit number)

21670229580835851942…87316794578003558401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

4.334 × 10⁹⁸(99-digit number)

43340459161671703885…74633589156007116801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

8.668 × 10⁹⁸(99-digit number)

86680918323343407770…49267178312014233601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.733 × 10⁹⁹(100-digit number)

17336183664668681554…98534356624028467201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

3.467 × 10⁹⁹(100-digit number)

34672367329337363108…97068713248056934401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

6.934 × 10⁹⁹(100-digit number)

69344734658674726216…94137426496113868801

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