Block #458,897

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/24/2014, 10:20:55 PM · Difficulty 10.4203 · 6,331,073 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

544584d48a4a1349a99a44dab3437e333be25d931e9a61dd731891e83d37c879

View on Chainz ↗

Height

#458,897

Difficulty

10.420295

Transactions

Size

1015 B

Version

Bits

0a6b9875

Nonce

5,201,980

Timestamp

3/24/2014, 10:20:55 PM

Confirmations

6,331,073

Merkle Root

4117dea59b6b6c1f25ae83345699d0a9defd583d2da4ddd0ac94a5395de1425f

Transactions (2)

Coinbase64eb069f87feaf…eea4e6a795aa68

1 in → 1 out9.2100 XPM109 B

AKBA1ztx…V2696eWt

aeac3636675e33…9ac8360c5bba46

5 in → 2 out288.2686 XPM816 B

AX6CZSTJ…sRPhjbPg AcJfu9Hn…b4QPwW2B

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.

3.937 × 10⁹⁵(96-digit number)

39371737658720521288…34556711222616164481

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

3.937 × 10⁹⁵(96-digit number)

39371737658720521288…34556711222616164481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

7.874 × 10⁹⁵(96-digit number)

78743475317441042577…69113422445232328961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.574 × 10⁹⁶(97-digit number)

15748695063488208515…38226844890464657921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

3.149 × 10⁹⁶(97-digit number)

31497390126976417030…76453689780929315841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

6.299 × 10⁹⁶(97-digit number)

62994780253952834061…52907379561858631681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.259 × 10⁹⁷(98-digit number)

12598956050790566812…05814759123717263361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.519 × 10⁹⁷(98-digit number)

25197912101581133624…11629518247434526721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

5.039 × 10⁹⁷(98-digit number)

50395824203162267249…23259036494869053441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.007 × 10⁹⁸(99-digit number)

10079164840632453449…46518072989738106881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

2.015 × 10⁹⁸(99-digit number)

20158329681264906899…93036145979476213761

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 Second 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 2CC formula:

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

Cross-reference on Chainz Explorer