Block #596,904

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 6/21/2014, 12:06:06 PM · Difficulty 10.9338 · 6,213,077 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d59baedec6c85e822e64644e6ff5e1b3a3d498d0a7a9e521cb112252ecf50736

Height

#596,904

Difficulty

10.933810

Transactions

3

Size

660 B

Version

2

Bits

0aef0e24

Nonce

785,447,090

Timestamp

6/21/2014, 12:06:06 PM

Confirmations

6,213,077

Merkle Root

d34f8796fbd90b2a3ae3a28177069d6ba53ee83056e497803fe429b198fd2569
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.

9.843 × 10⁹⁸(99-digit number)
98432677555868329619…85101786753193128319
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
9.843 × 10⁹⁸(99-digit number)
98432677555868329619…85101786753193128319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.968 × 10⁹⁹(100-digit number)
19686535511173665923…70203573506386256639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.937 × 10⁹⁹(100-digit number)
39373071022347331847…40407147012772513279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
7.874 × 10⁹⁹(100-digit number)
78746142044694663695…80814294025545026559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.574 × 10¹⁰⁰(101-digit number)
15749228408938932739…61628588051090053119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
3.149 × 10¹⁰⁰(101-digit number)
31498456817877865478…23257176102180106239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
6.299 × 10¹⁰⁰(101-digit number)
62996913635755730956…46514352204360212479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.259 × 10¹⁰¹(102-digit number)
12599382727151146191…93028704408720424959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.519 × 10¹⁰¹(102-digit number)
25198765454302292382…86057408817440849919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
5.039 × 10¹⁰¹(102-digit number)
50397530908604584765…72114817634881699839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
1.007 × 10¹⁰²(103-digit number)
10079506181720916953…44229635269763399679
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:57,723,920 XPM·at block #6,809,980 · updates every 60s
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