Block #169,831

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 9/18/2013, 7:39:33 AM · Difficulty 9.8669 · 6,626,512 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

0e8694d63da397d0d8400b9c0e7bb59fabef337f63fb4ad16b96169dba353f32

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Height

#169,831

Difficulty

9.866862

Transactions

Size

1.14 KB

Version

Bits

09ddeaaa

Nonce

105,374

Timestamp

9/18/2013, 7:39:33 AM

Confirmations

6,626,512

Mined by

⛏️ P2SHAWQaKbvUshfw8Fg8RHSe1zzEQ3f9MpbvV1

Merkle Root

cadf001b96e10bb21794628e56d58047e504edbea4e1279abb82fdc7dbed453e

Transactions (2)

Coinbasea10eac9b9dff74…fc043e4c8c4c40

1 in → 1 out10.2700 XPM109 B

AWQaKbvU…f9MpbvV1

1e239a28ffd0c2…a4ac4a4bda7ec0

6 in → 2 out5.0314 XPM966 B

AH3dDrPX…iXBYe8ZV AKzKWa6H…c4DCRtiu

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.

2.010 × 10⁹³(94-digit number)

20100558642361071554…43180528451909598931

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

2.010 × 10⁹³(94-digit number)

20100558642361071554…43180528451909598931

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

4.020 × 10⁹³(94-digit number)

40201117284722143109…86361056903819197861

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

8.040 × 10⁹³(94-digit number)

80402234569444286218…72722113807638395721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.608 × 10⁹⁴(95-digit number)

16080446913888857243…45444227615276791441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

3.216 × 10⁹⁴(95-digit number)

32160893827777714487…90888455230553582881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

6.432 × 10⁹⁴(95-digit number)

64321787655555428974…81776910461107165761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.286 × 10⁹⁵(96-digit number)

12864357531111085794…63553820922214331521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.572 × 10⁹⁵(96-digit number)

25728715062222171589…27107641844428663041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

5.145 × 10⁹⁵(96-digit number)

51457430124444343179…54215283688857326081

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