Block #373,911

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/24/2014, 3:26:44 PM · Difficulty 10.4266 · 6,434,790 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e5dd5b052a8f5d2ed90849af9c236ff441950e3b502c418183951c5139810cc5

Height

#373,911

Difficulty

10.426551

Transactions

5

Size

2.53 KB

Version

2

Bits

0a6d3279

Nonce

439,045

Timestamp

1/24/2014, 3:26:44 PM

Confirmations

6,434,790

Merkle Root

33f836613aac6a8d36349a1ea3f2166f1b755203af87794e5f81985d7d523030
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.

7.893 × 10⁹⁸(99-digit number)
78939538316133030485…10856982513956429121
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
7.893 × 10⁹⁸(99-digit number)
78939538316133030485…10856982513956429121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.578 × 10⁹⁹(100-digit number)
15787907663226606097…21713965027912858241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.157 × 10⁹⁹(100-digit number)
31575815326453212194…43427930055825716481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
6.315 × 10⁹⁹(100-digit number)
63151630652906424388…86855860111651432961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.263 × 10¹⁰⁰(101-digit number)
12630326130581284877…73711720223302865921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.526 × 10¹⁰⁰(101-digit number)
25260652261162569755…47423440446605731841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
5.052 × 10¹⁰⁰(101-digit number)
50521304522325139510…94846880893211463681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.010 × 10¹⁰¹(102-digit number)
10104260904465027902…89693761786422927361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.020 × 10¹⁰¹(102-digit number)
20208521808930055804…79387523572845854721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
4.041 × 10¹⁰¹(102-digit number)
40417043617860111608…58775047145691709441
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:57,713,658 XPM·at block #6,808,700 · updates every 60s
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