Block #1,241,386

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 9/17/2015, 11:36:28 PM · Difficulty 10.7560 · 5,576,581 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3e6c492fa0ee62ce4f2d8965da17137186ccaa8e3dc1c49ece2c21239f5c8b2e

Height

#1,241,386

Difficulty

10.755950

Transactions

3

Size

807 B

Version

2

Bits

0ac185f5

Nonce

178,089,050

Timestamp

9/17/2015, 11:36:28 PM

Confirmations

5,576,581

Merkle Root

96798fa62363b594cf588111c8fc918563185d115beb37c1149b878190604ad4
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.

2.054 × 10⁹⁶(97-digit number)
20544333988627875806…89043957567204834241
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
2.054 × 10⁹⁶(97-digit number)
20544333988627875806…89043957567204834241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
4.108 × 10⁹⁶(97-digit number)
41088667977255751613…78087915134409668481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
8.217 × 10⁹⁶(97-digit number)
82177335954511503226…56175830268819336961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.643 × 10⁹⁷(98-digit number)
16435467190902300645…12351660537638673921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.287 × 10⁹⁷(98-digit number)
32870934381804601290…24703321075277347841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
6.574 × 10⁹⁷(98-digit number)
65741868763609202580…49406642150554695681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.314 × 10⁹⁸(99-digit number)
13148373752721840516…98813284301109391361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.629 × 10⁹⁸(99-digit number)
26296747505443681032…97626568602218782721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
5.259 × 10⁹⁸(99-digit number)
52593495010887362064…95253137204437565441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.051 × 10⁹⁹(100-digit number)
10518699002177472412…90506274408875130881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
2.103 × 10⁹⁹(100-digit number)
21037398004354944825…81012548817750261761
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,787,806 XPM·at block #6,817,966 · updates every 60s
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