Block #485,344

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/11/2014, 12:20:15 AM · Difficulty 10.6070 · 6,322,750 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
558d93c137e32931e0a818c6c773e1ae277f86b0abc84ae808d0493a336a3e22

Height

#485,344

Difficulty

10.607041

Transactions

5

Size

4.89 KB

Version

2

Bits

0a9b6702

Nonce

9,198

Timestamp

4/11/2014, 12:20:15 AM

Confirmations

6,322,750

Merkle Root

65319833511b49d1c7fd574a95d7500bc50db3168b757d9d23d85029cbda1059
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.

8.755 × 10¹⁰⁰(101-digit number)
87559728610059313028…37050669912606340481
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.

1
origin + 1
8.755 × 10¹⁰⁰(101-digit number)
87559728610059313028…37050669912606340481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.751 × 10¹⁰¹(102-digit number)
17511945722011862605…74101339825212680961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.502 × 10¹⁰¹(102-digit number)
35023891444023725211…48202679650425361921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
7.004 × 10¹⁰¹(102-digit number)
70047782888047450423…96405359300850723841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.400 × 10¹⁰²(103-digit number)
14009556577609490084…92810718601701447681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.801 × 10¹⁰²(103-digit number)
28019113155218980169…85621437203402895361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
5.603 × 10¹⁰²(103-digit number)
56038226310437960338…71242874406805790721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.120 × 10¹⁰³(104-digit number)
11207645262087592067…42485748813611581441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.241 × 10¹⁰³(104-digit number)
22415290524175184135…84971497627223162881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
4.483 × 10¹⁰³(104-digit number)
44830581048350368270…69942995254446325761
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, …
Circulating Supply:57,708,798 XPM·at block #6,808,093 · updates every 60s
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