Block #391,695

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/6/2014, 12:01:00 AM · Difficulty 10.4311 · 6,433,202 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
0f69b60db0e8503ab9451cb37a0757c236a419510185f9f0699d3e0c74889f80

Height

#391,695

Difficulty

10.431094

Transactions

4

Size

1.64 KB

Version

2

Bits

0a6e5c34

Nonce

106,176

Timestamp

2/6/2014, 12:01:00 AM

Confirmations

6,433,202

Merkle Root

f460dd0c76bdbbfb32224d3d7b2989ea429c0295b9d74b385578a83db607fe6e
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.

1.414 × 10⁹⁶(97-digit number)
14143068263118996282…54872055616617167679
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
1.414 × 10⁹⁶(97-digit number)
14143068263118996282…54872055616617167679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.828 × 10⁹⁶(97-digit number)
28286136526237992564…09744111233234335359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
5.657 × 10⁹⁶(97-digit number)
56572273052475985128…19488222466468670719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.131 × 10⁹⁷(98-digit number)
11314454610495197025…38976444932937341439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.262 × 10⁹⁷(98-digit number)
22628909220990394051…77952889865874682879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
4.525 × 10⁹⁷(98-digit number)
45257818441980788102…55905779731749365759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
9.051 × 10⁹⁷(98-digit number)
90515636883961576205…11811559463498731519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.810 × 10⁹⁸(99-digit number)
18103127376792315241…23623118926997463039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
3.620 × 10⁹⁸(99-digit number)
36206254753584630482…47246237853994926079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
7.241 × 10⁹⁸(99-digit number)
72412509507169260964…94492475707989852159
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:57,843,258 XPM·at block #6,824,896 · 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