Block #494,337

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/16/2014, 3:10:59 AM · Difficulty 10.7167 · 6,307,897 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a76e87618f5124a98e872fa8cec4aeac0eef81947fc3dc98ee6de73db043832e

Height

#494,337

Difficulty

10.716724

Transactions

4

Size

7.92 KB

Version

2

Bits

0ab77b3c

Nonce

204,454,020

Timestamp

4/16/2014, 3:10:59 AM

Confirmations

6,307,897

Merkle Root

3d887c564292651516a1f10e144173173517cfcd187627ffb974a373e7cb99a0
Transactions (4)
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.

3.970 × 10⁹⁷(98-digit number)
39709693066225286525…78189286709402180599
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
3.970 × 10⁹⁷(98-digit number)
39709693066225286525…78189286709402180599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
7.941 × 10⁹⁷(98-digit number)
79419386132450573050…56378573418804361199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.588 × 10⁹⁸(99-digit number)
15883877226490114610…12757146837608722399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
3.176 × 10⁹⁸(99-digit number)
31767754452980229220…25514293675217444799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
6.353 × 10⁹⁸(99-digit number)
63535508905960458440…51028587350434889599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.270 × 10⁹⁹(100-digit number)
12707101781192091688…02057174700869779199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.541 × 10⁹⁹(100-digit number)
25414203562384183376…04114349401739558399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
5.082 × 10⁹⁹(100-digit number)
50828407124768366752…08228698803479116799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.016 × 10¹⁰⁰(101-digit number)
10165681424953673350…16457397606958233599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
2.033 × 10¹⁰⁰(101-digit number)
20331362849907346700…32914795213916467199
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 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
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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,661,880 XPM·at block #6,802,233 · updates every 60s
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