Block #244,680

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 11/5/2013, 12:40:42 AM · Difficulty 9.9631 · 6,598,621 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
81c3029f406b23f671841f905f93206cb3b9143de7f86c08bff49898f0372f51

Height

#244,680

Difficulty

9.963065

Transactions

3

Size

682 B

Version

2

Bits

09f68b6e

Nonce

9,332

Timestamp

11/5/2013, 12:40:42 AM

Confirmations

6,598,621

Merkle Root

02e4b7ab3d8b0766db90f1a7a9ac87bd3566431304d8569381fd113c3a2af01b
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.

2.389 × 10¹⁰¹(102-digit number)
23895420817062135606…46206560623993855999
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
2.389 × 10¹⁰¹(102-digit number)
23895420817062135606…46206560623993855999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
4.779 × 10¹⁰¹(102-digit number)
47790841634124271213…92413121247987711999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
9.558 × 10¹⁰¹(102-digit number)
95581683268248542427…84826242495975423999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.911 × 10¹⁰²(103-digit number)
19116336653649708485…69652484991950847999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
3.823 × 10¹⁰²(103-digit number)
38232673307299416970…39304969983901695999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
7.646 × 10¹⁰²(103-digit number)
76465346614598833941…78609939967803391999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.529 × 10¹⁰³(104-digit number)
15293069322919766788…57219879935606783999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
3.058 × 10¹⁰³(104-digit number)
30586138645839533576…14439759871213567999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
6.117 × 10¹⁰³(104-digit number)
61172277291679067153…28879519742427135999
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:57,990,773 XPM·at block #6,843,300 · updates every 60s
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