Block #1,197,054

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 8/16/2015, 11:51:32 PM · Difficulty 10.8260 · 5,630,184 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
46b1266a074a54ddd5ab6f8896e5522def7e5dc9eaacbe5bc66dc35ae3ad5da8

Height

#1,197,054

Difficulty

10.825976

Transactions

2

Size

2.00 KB

Version

2

Bits

0ad3732d

Nonce

260,183,572

Timestamp

8/16/2015, 11:51:32 PM

Confirmations

5,630,184

Merkle Root

127ff4339fe4cc676ceeaf174aea1bde21ba6d641c4d6d489e2915362d003fd1
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.

1.794 × 10⁹³(94-digit number)
17944331441921341736…10246889905483722781
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
1.794 × 10⁹³(94-digit number)
17944331441921341736…10246889905483722781
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
3.588 × 10⁹³(94-digit number)
35888662883842683472…20493779810967445561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
7.177 × 10⁹³(94-digit number)
71777325767685366944…40987559621934891121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.435 × 10⁹⁴(95-digit number)
14355465153537073388…81975119243869782241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.871 × 10⁹⁴(95-digit number)
28710930307074146777…63950238487739564481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
5.742 × 10⁹⁴(95-digit number)
57421860614148293555…27900476975479128961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.148 × 10⁹⁵(96-digit number)
11484372122829658711…55800953950958257921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.296 × 10⁹⁵(96-digit number)
22968744245659317422…11601907901916515841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
4.593 × 10⁹⁵(96-digit number)
45937488491318634844…23203815803833031681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
9.187 × 10⁹⁵(96-digit number)
91874976982637269688…46407631607666063361
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:57,862,005 XPM·at block #6,827,237 · 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