Block #1,105,983

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 6/15/2015, 6:13:49 AM · Difficulty 10.7906 · 5,702,400 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8dbbdb1db19214038a244501ef8e2894296c9acd2cf23e52784fce1f61bbec86

Height

#1,105,983

Difficulty

10.790568

Transactions

43

Size

16.39 KB

Version

2

Bits

0aca62b1

Nonce

90,343,086

Timestamp

6/15/2015, 6:13:49 AM

Confirmations

5,702,400

Merkle Root

b054c46242f0234c7d4567b7aef2e67a7d273866b440df7830a4af8889dcb9bc
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.

2.574 × 10⁹⁴(95-digit number)
25742910032869349731…30971495898878239519
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
2.574 × 10⁹⁴(95-digit number)
25742910032869349731…30971495898878239519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
5.148 × 10⁹⁴(95-digit number)
51485820065738699462…61942991797756479039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.029 × 10⁹⁵(96-digit number)
10297164013147739892…23885983595512958079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.059 × 10⁹⁵(96-digit number)
20594328026295479784…47771967191025916159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
4.118 × 10⁹⁵(96-digit number)
41188656052590959569…95543934382051832319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
8.237 × 10⁹⁵(96-digit number)
82377312105181919139…91087868764103664639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.647 × 10⁹⁶(97-digit number)
16475462421036383827…82175737528207329279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
3.295 × 10⁹⁶(97-digit number)
32950924842072767655…64351475056414658559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
6.590 × 10⁹⁶(97-digit number)
65901849684145535311…28702950112829317119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.318 × 10⁹⁷(98-digit number)
13180369936829107062…57405900225658634239
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:57,711,118 XPM·at block #6,808,382 · 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.

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