Block #377,750

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/27/2014, 8:41:13 AM · Difficulty 10.4189 · 6,447,965 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
11ed668faa7afd97c2247c9c35702fb2ce67abcaebbe41bc83f315fa2a732308

Height

#377,750

Difficulty

10.418862

Transactions

1

Size

937 B

Version

2

Bits

0a6b3a82

Nonce

6,668

Timestamp

1/27/2014, 8:41:13 AM

Confirmations

6,447,965

Merkle Root

08df23056446d936e762d32384a3a6a1dce78aba8662b38fd40e61f67f0f1057
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.

5.677 × 10⁹⁸(99-digit number)
56778027041547471220…24431193848315714401
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
5.677 × 10⁹⁸(99-digit number)
56778027041547471220…24431193848315714401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.135 × 10⁹⁹(100-digit number)
11355605408309494244…48862387696631428801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.271 × 10⁹⁹(100-digit number)
22711210816618988488…97724775393262857601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
4.542 × 10⁹⁹(100-digit number)
45422421633237976976…95449550786525715201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
9.084 × 10⁹⁹(100-digit number)
90844843266475953952…90899101573051430401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.816 × 10¹⁰⁰(101-digit number)
18168968653295190790…81798203146102860801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.633 × 10¹⁰⁰(101-digit number)
36337937306590381581…63596406292205721601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
7.267 × 10¹⁰⁰(101-digit number)
72675874613180763162…27192812584411443201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.453 × 10¹⁰¹(102-digit number)
14535174922636152632…54385625168822886401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.907 × 10¹⁰¹(102-digit number)
29070349845272305264…08771250337645772801
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:57,849,825 XPM·at block #6,825,714 · 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