Block #1,442,656

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/4/2016, 8:06:59 PM · Difficulty 10.7599 · 5,402,491 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9aa936c1180c1566a8a26d1c9f5d474fe694c070291f05dc71c3a1f44fc5274c

Height

#1,442,656

Difficulty

10.759874

Transactions

2

Size

1.08 KB

Version

2

Bits

0ac2871d

Nonce

1,980,460,081

Timestamp

2/4/2016, 8:06:59 PM

Confirmations

5,402,491

Merkle Root

d298108569f9bd5167539acec48c49db95626dbf727c7d708690c54f6cbdc20e
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.

1.725 × 10⁹⁴(95-digit number)
17251245805570644357…27786112636037656879
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
1.725 × 10⁹⁴(95-digit number)
17251245805570644357…27786112636037656879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
3.450 × 10⁹⁴(95-digit number)
34502491611141288714…55572225272075313759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
6.900 × 10⁹⁴(95-digit number)
69004983222282577428…11144450544150627519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.380 × 10⁹⁵(96-digit number)
13800996644456515485…22288901088301255039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.760 × 10⁹⁵(96-digit number)
27601993288913030971…44577802176602510079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
5.520 × 10⁹⁵(96-digit number)
55203986577826061942…89155604353205020159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.104 × 10⁹⁶(97-digit number)
11040797315565212388…78311208706410040319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.208 × 10⁹⁶(97-digit number)
22081594631130424777…56622417412820080639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
4.416 × 10⁹⁶(97-digit number)
44163189262260849554…13244834825640161279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
8.832 × 10⁹⁶(97-digit number)
88326378524521699108…26489669651280322559
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:58,005,602 XPM·at block #6,845,146 · 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