Block #340,363

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/2/2014, 5:53:19 PM · Difficulty 10.1309 · 6,486,305 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

f9ff20c68a86b5f5fc7c0c139056d64baf74365cc860ad7b10ba3fbc7e656504

View on Chainz ↗

Height

#340,363

Difficulty

10.130892

Transactions

Size

210 B

Version

Bits

0a21822b

Nonce

22,604

Timestamp

1/2/2014, 5:53:19 PM

Confirmations

6,486,305

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

305dec4070d2d35afd31c5f693a48e2edc3eb44a64c04ac1256bc86b41648471

Transactions (1)

Coinbase305dec4070d2d3…6bc86b41648471

1 in → 1 out9.7300 XPM116 B

AbwWkWZt…kawDhufa

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.

2.727 × 10¹⁰⁴(105-digit number)

27271119637992137860…63407614335638348279

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

2.727 × 10¹⁰⁴(105-digit number)

27271119637992137860…63407614335638348279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

5.454 × 10¹⁰⁴(105-digit number)

54542239275984275721…26815228671276696559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.090 × 10¹⁰⁵(106-digit number)

10908447855196855144…53630457342553393119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.181 × 10¹⁰⁵(106-digit number)

21816895710393710288…07260914685106786239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

4.363 × 10¹⁰⁵(106-digit number)

43633791420787420577…14521829370213572479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

8.726 × 10¹⁰⁵(106-digit number)

87267582841574841154…29043658740427144959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.745 × 10¹⁰⁶(107-digit number)

17453516568314968230…58087317480854289919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.490 × 10¹⁰⁶(107-digit number)

34907033136629936461…16174634961708579839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

6.981 × 10¹⁰⁶(107-digit number)

69814066273259872923…32349269923417159679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.396 × 10¹⁰⁷(108-digit number)

13962813254651974584…64698539846834319359

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 First 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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …

Cross-reference on Chainz Explorer

Block #340,363

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