Block #475,308

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/5/2014, 3:54:16 AM · Difficulty 10.4556 · 6,328,221 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

5f9c5d713ac2ba90d69e43be9daa6893a504061665d5967db3e5a2b94ca36a23

View on Chainz ↗

Height

#475,308

Difficulty

10.455612

Transactions

Size

968 B

Version

Bits

0a74a300

Nonce

138,654

Timestamp

4/5/2014, 3:54:16 AM

Confirmations

6,328,221

Mined by

AGz9gyZWgxBxAyVrKrWDzMw21kbo8NYQpw

Merkle Root

0783c35b0bb9d4050ba27717fa6c7e2cea235201d0d7e1ae979e2c1e137fda47

Transactions (1)

Coinbase0783c35b0bb9d4…9e2c1e137fda47

1 in → 24 out9.1300 XPM879 B

AGz9gyZW…bo8NYQpw AdFLJFhb…bsaVkAyh AUFKXvnz…342ApNcm AH5mD99t…Spv1yg4N ATp4jJhs…TbSgR8Qb

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.

3.033 × 10⁹²(93-digit number)

30339793708824369780…05746943878456319999

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

3.033 × 10⁹²(93-digit number)

30339793708824369780…05746943878456319999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

6.067 × 10⁹²(93-digit number)

60679587417648739560…11493887756912639999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.213 × 10⁹³(94-digit number)

12135917483529747912…22987775513825279999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.427 × 10⁹³(94-digit number)

24271834967059495824…45975551027650559999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

4.854 × 10⁹³(94-digit number)

48543669934118991648…91951102055301119999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

9.708 × 10⁹³(94-digit number)

97087339868237983296…83902204110602239999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.941 × 10⁹⁴(95-digit number)

19417467973647596659…67804408221204479999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.883 × 10⁹⁴(95-digit number)

38834935947295193318…35608816442408959999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

7.766 × 10⁹⁴(95-digit number)

77669871894590386637…71217632884817919999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.553 × 10⁹⁵(96-digit number)

15533974378918077327…42435265769635839999

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