Block #184,989

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 9/29/2013, 12:03:15 AM · Difficulty 9.8620 · 6,611,118 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
5e362a111b33e14515aa3f9ccca5dbb7f2e724276869f8401b8fc08250d529dd

Height

#184,989

Difficulty

9.862037

Transactions

4

Size

877 B

Version

2

Bits

09dcae7c

Nonce

70,228

Timestamp

9/29/2013, 12:03:15 AM

Confirmations

6,611,118

Merkle Root

950228f5fa5277b733cbb69afde3352b0c73faf22d7c456e117b62d6ec0a45cd
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.

1.135 × 10⁹⁷(98-digit number)
11355686860452855997…39186325447701646539
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
1.135 × 10⁹⁷(98-digit number)
11355686860452855997…39186325447701646539
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.271 × 10⁹⁷(98-digit number)
22711373720905711995…78372650895403293079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
4.542 × 10⁹⁷(98-digit number)
45422747441811423990…56745301790806586159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
9.084 × 10⁹⁷(98-digit number)
90845494883622847981…13490603581613172319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.816 × 10⁹⁸(99-digit number)
18169098976724569596…26981207163226344639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
3.633 × 10⁹⁸(99-digit number)
36338197953449139192…53962414326452689279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
7.267 × 10⁹⁸(99-digit number)
72676395906898278385…07924828652905378559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.453 × 10⁹⁹(100-digit number)
14535279181379655677…15849657305810757119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.907 × 10⁹⁹(100-digit number)
29070558362759311354…31699314611621514239
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,612,850 XPM·at block #6,796,106 · updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.