Block #508,596

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 4/24/2014, 11:59:56 AM · Difficulty 10.8190 · 6,296,617 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2806ed98b01473605d85e8cd1e420558fd942d586b460219dd2384468e9d3ca7

Height

#508,596

Difficulty

10.818965

Transactions

4

Size

881 B

Version

2

Bits

0ad1a7a9

Nonce

340,592

Timestamp

4/24/2014, 11:59:56 AM

Confirmations

6,296,617

Merkle Root

5c6565faa97eb055eb6b6ac7c12577b70df5ab0657f0086a19288ae16fbd5bcb
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.

7.062 × 10¹⁰¹(102-digit number)
70622575512449568824…41860973323176268799
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
7.062 × 10¹⁰¹(102-digit number)
70622575512449568824…41860973323176268799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.412 × 10¹⁰²(103-digit number)
14124515102489913764…83721946646352537599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.824 × 10¹⁰²(103-digit number)
28249030204979827529…67443893292705075199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
5.649 × 10¹⁰²(103-digit number)
56498060409959655059…34887786585410150399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.129 × 10¹⁰³(104-digit number)
11299612081991931011…69775573170820300799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.259 × 10¹⁰³(104-digit number)
22599224163983862023…39551146341640601599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
4.519 × 10¹⁰³(104-digit number)
45198448327967724047…79102292683281203199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
9.039 × 10¹⁰³(104-digit number)
90396896655935448095…58204585366562406399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.807 × 10¹⁰⁴(105-digit number)
18079379331187089619…16409170733124812799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
3.615 × 10¹⁰⁴(105-digit number)
36158758662374179238…32818341466249625599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
7.231 × 10¹⁰⁴(105-digit number)
72317517324748358476…65636682932499251199
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 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
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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,685,777 XPM·at block #6,805,212 · updates every 60s
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