Block #463,063

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/27/2014, 8:21:48 PM · Difficulty 10.4188 · 6,344,546 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

58cac0443bb78132b42f66c512817537dd9dc33f4550d56950724a02a1f4edad

View on Chainz ↗

Height

#463,063

Difficulty

10.418769

Transactions

Size

902 B

Version

Bits

0a6b3477

Nonce

20,166

Timestamp

3/27/2014, 8:21:48 PM

Confirmations

6,344,546

Mined by

AdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

8656e374430a17733853de09fc9662caf9115c1f44e4aaafaef32ce1ca84bef4

Transactions (1)

Coinbase8656e374430a17…f32ce1ca84bef4

1 in → 22 out9.2000 XPM811 B

AdFLJFhb…bsaVkAyh AGz9gyZW…bo8NYQpw ASgUri65…C7NLcyBg APtc8nU2…tp6qFHwW AUDD9tmA…gJPQLnsz

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.

3.652 × 10⁹⁷(98-digit number)

36523976943146756565…41690309651569132799

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

3.652 × 10⁹⁷(98-digit number)

36523976943146756565…41690309651569132799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

7.304 × 10⁹⁷(98-digit number)

73047953886293513130…83380619303138265599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.460 × 10⁹⁸(99-digit number)

14609590777258702626…66761238606276531199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.921 × 10⁹⁸(99-digit number)

29219181554517405252…33522477212553062399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

5.843 × 10⁹⁸(99-digit number)

58438363109034810504…67044954425106124799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.168 × 10⁹⁹(100-digit number)

11687672621806962100…34089908850212249599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.337 × 10⁹⁹(100-digit number)

23375345243613924201…68179817700424499199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

4.675 × 10⁹⁹(100-digit number)

46750690487227848403…36359635400848998399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

9.350 × 10⁹⁹(100-digit number)

93501380974455696806…72719270801697996799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.870 × 10¹⁰⁰(101-digit number)

18700276194891139361…45438541603395993599

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 #463,063

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