Block #1,315,565

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/6/2015, 1:03:58 PM · Difficulty 10.8623 · 5,497,437 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d3cc722e48e988965c7e89c365781f19ad311ec336a2d34fcde50bca2903dee9

Height

#1,315,565

Difficulty

10.862275

Transactions

2

Size

834 B

Version

2

Bits

0adcbe0b

Nonce

171,399,842

Timestamp

11/6/2015, 1:03:58 PM

Confirmations

5,497,437

Merkle Root

37be3e2eb035b7a98c8abd5f66fa160bcc82e3608a00915ae862183a0fc576c4
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.

2.057 × 10⁹⁶(97-digit number)
20571505540127681784…57205100226029248001
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
2.057 × 10⁹⁶(97-digit number)
20571505540127681784…57205100226029248001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
4.114 × 10⁹⁶(97-digit number)
41143011080255363569…14410200452058496001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
8.228 × 10⁹⁶(97-digit number)
82286022160510727138…28820400904116992001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.645 × 10⁹⁷(98-digit number)
16457204432102145427…57640801808233984001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.291 × 10⁹⁷(98-digit number)
32914408864204290855…15281603616467968001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
6.582 × 10⁹⁷(98-digit number)
65828817728408581710…30563207232935936001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.316 × 10⁹⁸(99-digit number)
13165763545681716342…61126414465871872001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.633 × 10⁹⁸(99-digit number)
26331527091363432684…22252828931743744001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
5.266 × 10⁹⁸(99-digit number)
52663054182726865368…44505657863487488001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.053 × 10⁹⁹(100-digit number)
10532610836545373073…89011315726974976001
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:57,748,056 XPM·at block #6,813,001 · 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