Block #946,105

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/21/2015, 2:26:34 PM · Difficulty 10.8985 · 5,863,951 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7f54c9d09900bf0e20dab2fcfbad77a6995798fa1de1abea0d5f7be34e031ab5

Height

#946,105

Difficulty

10.898520

Transactions

3

Size

945 B

Version

2

Bits

0ae60570

Nonce

371,353,158

Timestamp

2/21/2015, 2:26:34 PM

Confirmations

5,863,951

Merkle Root

a19a42f056807ef6ef0e059982a5ffdd4b47b85e1f41f01d43050798e4d7ea45
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.

1.538 × 10⁹³(94-digit number)
15380194254721305135…08388694045108725281
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
1.538 × 10⁹³(94-digit number)
15380194254721305135…08388694045108725281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
3.076 × 10⁹³(94-digit number)
30760388509442610271…16777388090217450561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
6.152 × 10⁹³(94-digit number)
61520777018885220542…33554776180434901121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.230 × 10⁹⁴(95-digit number)
12304155403777044108…67109552360869802241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.460 × 10⁹⁴(95-digit number)
24608310807554088216…34219104721739604481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
4.921 × 10⁹⁴(95-digit number)
49216621615108176433…68438209443479208961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
9.843 × 10⁹⁴(95-digit number)
98433243230216352867…36876418886958417921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.968 × 10⁹⁵(96-digit number)
19686648646043270573…73752837773916835841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.937 × 10⁹⁵(96-digit number)
39373297292086541147…47505675547833671681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
7.874 × 10⁹⁵(96-digit number)
78746594584173082294…95011351095667343361
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:57,724,521 XPM·at block #6,810,055 · updates every 60s
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