Block #1,206,355

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 8/24/2015, 5:29:06 AM · Difficulty 10.7830 · 5,607,876 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
828c86b912db2c25643d17d9d062fd7d47116c0ded230091ac9d26339f484d56

Height

#1,206,355

Difficulty

10.783019

Transactions

2

Size

3.89 KB

Version

2

Bits

0ac873e7

Nonce

450,323,702

Timestamp

8/24/2015, 5:29:06 AM

Confirmations

5,607,876

Merkle Root

3191737bb6a6603b03cfdaf33e42ffc0a6121e2ad029b74cee2fb41d90ff523f
Transactions (2)
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.

7.936 × 10⁹²(93-digit number)
79363714151997066099…11453830687159862321
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
7.936 × 10⁹²(93-digit number)
79363714151997066099…11453830687159862321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.587 × 10⁹³(94-digit number)
15872742830399413219…22907661374319724641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.174 × 10⁹³(94-digit number)
31745485660798826439…45815322748639449281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
6.349 × 10⁹³(94-digit number)
63490971321597652879…91630645497278898561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.269 × 10⁹⁴(95-digit number)
12698194264319530575…83261290994557797121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.539 × 10⁹⁴(95-digit number)
25396388528639061151…66522581989115594241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
5.079 × 10⁹⁴(95-digit number)
50792777057278122303…33045163978231188481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.015 × 10⁹⁵(96-digit number)
10158555411455624460…66090327956462376961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.031 × 10⁹⁵(96-digit number)
20317110822911248921…32180655912924753921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
4.063 × 10⁹⁵(96-digit number)
40634221645822497843…64361311825849507841
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:57,757,919 XPM·at block #6,814,230 · updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
Privacy Policy·

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

·Privacy Policy