Block #393,270

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/7/2014, 1:18:21 AM · Difficulty 10.4378 · 6,413,470 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

02734919d36cd234838fe15f350b4a1ee8561d4a9938ecb409ecc3cc3483e819

View on Chainz ↗

Height

#393,270

Difficulty

10.437838

Transactions

Size

202 B

Version

Bits

0a701628

Nonce

8,148

Timestamp

2/7/2014, 1:18:21 AM

Confirmations

6,413,470

Mined by

⛏️ P2SHAb64gm8KUnFNR9oWChHpwHnuPjmwRnN1CH

Merkle Root

5bfc30b37435a90070bd4f551b73e647f1abfbf53d8eb8341e0305e41674b936

Transactions (1)

Coinbase5bfc30b37435a9…0305e41674b936

1 in → 1 out9.1600 XPM109 B

Ab64gm8K…mwRnN1CH

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.

3.854 × 10¹⁰¹(102-digit number)

38540205548324043090…44709286185322670339

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

3.854 × 10¹⁰¹(102-digit number)

38540205548324043090…44709286185322670339

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

7.708 × 10¹⁰¹(102-digit number)

77080411096648086180…89418572370645340679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.541 × 10¹⁰²(103-digit number)

15416082219329617236…78837144741290681359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

3.083 × 10¹⁰²(103-digit number)

30832164438659234472…57674289482581362719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

6.166 × 10¹⁰²(103-digit number)

61664328877318468944…15348578965162725439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.233 × 10¹⁰³(104-digit number)

12332865775463693788…30697157930325450879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.466 × 10¹⁰³(104-digit number)

24665731550927387577…61394315860650901759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

4.933 × 10¹⁰³(104-digit number)

49331463101854775155…22788631721301803519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

9.866 × 10¹⁰³(104-digit number)

98662926203709550311…45577263442603607039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.973 × 10¹⁰⁴(105-digit number)

19732585240741910062…91154526885207214079

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 #393,270

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