Block #385,649

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/1/2014, 10:25:19 PM · Difficulty 10.4071 · 6,439,986 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
9808c198e285a209bf330093b84ddbc9365aeab3325507ca0c206a3146864861

Height

#385,649

Difficulty

10.407115

Transactions

1

Size

934 B

Version

2

Bits

0a6838b0

Nonce

228,672

Timestamp

2/1/2014, 10:25:19 PM

Confirmations

6,439,986

Merkle Root

47fbd2b35c5fb3266ffca0c52a13d9325cddf834d5ff0c0b11b56937bd0b3dd4
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.

2.100 × 10⁹³(94-digit number)
21007837213319375879…38964258960888934401
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
2.100 × 10⁹³(94-digit number)
21007837213319375879…38964258960888934401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
4.201 × 10⁹³(94-digit number)
42015674426638751758…77928517921777868801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
8.403 × 10⁹³(94-digit number)
84031348853277503517…55857035843555737601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.680 × 10⁹⁴(95-digit number)
16806269770655500703…11714071687111475201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.361 × 10⁹⁴(95-digit number)
33612539541311001406…23428143374222950401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
6.722 × 10⁹⁴(95-digit number)
67225079082622002813…46856286748445900801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.344 × 10⁹⁵(96-digit number)
13445015816524400562…93712573496891801601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.689 × 10⁹⁵(96-digit number)
26890031633048801125…87425146993783603201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
5.378 × 10⁹⁵(96-digit number)
53780063266097602250…74850293987567206401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.075 × 10⁹⁶(97-digit number)
10756012653219520450…49700587975134412801
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:57,849,184 XPM·at block #6,825,634 · 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