Block #1,658,292

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/3/2016, 3:21:58 AM · Difficulty 10.7944 · 5,182,787 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

3e3175ddd4ec24002e8bf102c406f0b655763ea6b3e8e3a8f1a466c3a9a35c4f

View on Chainz ↗

Height

#1,658,292

Difficulty

10.794355

Transactions

Size

243 B

Version

Bits

0acb5add

Nonce

2,451,383,702

Timestamp

7/3/2016, 3:21:58 AM

Confirmations

5,182,787

Mined by

⛏️ P2SHAGdPoJeNQpJM3ACMJHD5qSzT98tYbQQJmT

Merkle Root

6400ae360b46b36448c3efa1b64ef713dca0d654f58b977e6631bd91c97fa63e

Transactions (1)

Coinbase6400ae360b46b3…31bd91c97fa63e

1 in → 2 out8.5700 XPM152 B

AGdPoJeN…tYbQQJmT AXbk7f7A…Tx7JECPG

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.

3.007 × 10⁹⁷(98-digit number)

30072110621786247820…92869920384755712001

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

3.007 × 10⁹⁷(98-digit number)

30072110621786247820…92869920384755712001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

6.014 × 10⁹⁷(98-digit number)

60144221243572495641…85739840769511424001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.202 × 10⁹⁸(99-digit number)

12028844248714499128…71479681539022848001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.405 × 10⁹⁸(99-digit number)

24057688497428998256…42959363078045696001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

4.811 × 10⁹⁸(99-digit number)

48115376994857996513…85918726156091392001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

9.623 × 10⁹⁸(99-digit number)

96230753989715993026…71837452312182784001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.924 × 10⁹⁹(100-digit number)

19246150797943198605…43674904624365568001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

3.849 × 10⁹⁹(100-digit number)

38492301595886397210…87349809248731136001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

7.698 × 10⁹⁹(100-digit number)

76984603191772794421…74699618497462272001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.539 × 10¹⁰⁰(101-digit number)

15396920638354558884…49399236994924544001

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

Block #1,658,292

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