Block #464,787

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/29/2014, 12:43:34 AM · Difficulty 10.4223 · 6,336,548 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

cfab35e209be22d15bb58e1213958519eaf79450d3c3b9258f25925547684b5a

View on Chainz ↗

Height

#464,787

Difficulty

10.422310

Transactions

Size

969 B

Version

Bits

0a6c1c7e

Nonce

368,257

Timestamp

3/29/2014, 12:43:34 AM

Confirmations

6,336,548

Mined by

⛏️ 6hAdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

2f4f467738a363138c2f6a8353ba9e9bd39f739f7cb23a06f7fc374506a47bb2

Transactions (1)

Coinbase2f4f467738a363…fc374506a47bb2

1 in → 24 out9.1900 XPM879 B

AdFLJFhb…bsaVkAyh APtc8nU2…tp6qFHwW AMW1p9oT…2TzdaZxH AUzEPJFG…kYkA5U9V ASgUri65…C7NLcyBg

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.

3.132 × 10⁹⁴(95-digit number)

31320605875429470722…14080464618926412159

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

3.132 × 10⁹⁴(95-digit number)

31320605875429470722…14080464618926412159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

6.264 × 10⁹⁴(95-digit number)

62641211750858941444…28160929237852824319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.252 × 10⁹⁵(96-digit number)

12528242350171788288…56321858475705648639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.505 × 10⁹⁵(96-digit number)

25056484700343576577…12643716951411297279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

5.011 × 10⁹⁵(96-digit number)

50112969400687153155…25287433902822594559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.002 × 10⁹⁶(97-digit number)

10022593880137430631…50574867805645189119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.004 × 10⁹⁶(97-digit number)

20045187760274861262…01149735611290378239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

4.009 × 10⁹⁶(97-digit number)

40090375520549722524…02299471222580756479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

8.018 × 10⁹⁶(97-digit number)

80180751041099445048…04598942445161512959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.603 × 10⁹⁷(98-digit number)

16036150208219889009…09197884890323025919

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