Block #88,069

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/29/2013, 8:25:00 AM · Difficulty 9.2742 · 6,717,023 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

5e96c5b8e5f34c11b6b225e9f3068bf8c6c830c5dcddd6b11b9dc35239e41a2b

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Height

#88,069

Difficulty

9.274150

Transactions

Size

1.00 KB

Version

Bits

09462eb2

Nonce

355,861

Timestamp

7/29/2013, 8:25:00 AM

Confirmations

6,717,023

Mined by

⛏️ P2SHAKFZhH2f7i5ULLvhP7w9w1daFjJBaegs5Q

Merkle Root

100ab7a6a2a042defaeb6435314e7d8b2f9361abe211b848e2ace5c2b7a3e949

Transactions (3)

Coinbased7731ecaee3396…84f544ce6129ac

1 in → 1 out11.6300 XPM109 B

AKFZhH2f…JBaegs5Q

332c9c5692726c…fc29db2c1d8a8e

4 in → 2 out514.0127 XPM668 B

ATbH2p6x…M1bnnu94 AdGYnqoY…pjMuwV34

6409c2c037b34d…b53b29339f7d82

1 in → 1 out11.5900 XPM158 B

ALqZ91rG…RtQ3C2x3

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.

1.958 × 10¹⁰⁵(106-digit number)

19586087221162277491…42064141601660543301

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

1.958 × 10¹⁰⁵(106-digit number)

19586087221162277491…42064141601660543301

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.917 × 10¹⁰⁵(106-digit number)

39172174442324554982…84128283203321086601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

7.834 × 10¹⁰⁵(106-digit number)

78344348884649109964…68256566406642173201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.566 × 10¹⁰⁶(107-digit number)

15668869776929821992…36513132813284346401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

3.133 × 10¹⁰⁶(107-digit number)

31337739553859643985…73026265626568692801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

6.267 × 10¹⁰⁶(107-digit number)

62675479107719287971…46052531253137385601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.253 × 10¹⁰⁷(108-digit number)

12535095821543857594…92105062506274771201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.507 × 10¹⁰⁷(108-digit number)

25070191643087715188…84210125012549542401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

5.014 × 10¹⁰⁷(108-digit number)

50140383286175430377…68420250025099084801

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