Block #366,107

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/19/2014, 5:11:58 AM · Difficulty 10.4258 · 6,451,363 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
42c927f597700ff9bd2d5c6ee6bb854900ff05a1627e83fc3af7a440ad7a92ce

Height

#366,107

Difficulty

10.425847

Transactions

2

Size

425 B

Version

2

Bits

0a6d044c

Nonce

326,709

Timestamp

1/19/2014, 5:11:58 AM

Confirmations

6,451,363

Merkle Root

bf7c20017c7eb65566398456eb3b7656f1024e308aa4e1607a4a85c621b835d7
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.

3.379 × 10⁹⁴(95-digit number)
33791252852489525476…22458465296245473279
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
3.379 × 10⁹⁴(95-digit number)
33791252852489525476…22458465296245473279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
6.758 × 10⁹⁴(95-digit number)
67582505704979050952…44916930592490946559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.351 × 10⁹⁵(96-digit number)
13516501140995810190…89833861184981893119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.703 × 10⁹⁵(96-digit number)
27033002281991620380…79667722369963786239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
5.406 × 10⁹⁵(96-digit number)
54066004563983240761…59335444739927572479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.081 × 10⁹⁶(97-digit number)
10813200912796648152…18670889479855144959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.162 × 10⁹⁶(97-digit number)
21626401825593296304…37341778959710289919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
4.325 × 10⁹⁶(97-digit number)
43252803651186592609…74683557919420579839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
8.650 × 10⁹⁶(97-digit number)
86505607302373185218…49367115838841159679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.730 × 10⁹⁷(98-digit number)
17301121460474637043…98734231677682319359
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 First 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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,783,811 XPM·at block #6,817,469 · 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