Block #192,559

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 10/3/2013, 11:09:55 PM · Difficulty 9.8745 · 6,606,909 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2a60f821d782ee3af6d0279e3867754f92e32280ac4873680296eb2259e57c3d

Height

#192,559

Difficulty

9.874510

Transactions

2

Size

4.70 KB

Version

2

Bits

09dfdfdf

Nonce

1,164,791,862

Timestamp

10/3/2013, 11:09:55 PM

Confirmations

6,606,909

Merkle Root

e6d8a89788ede80f286e4fdc61bf91cfbc0ff75c891a3a1b09db102801482f12
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.

9.907 × 10⁹⁸(99-digit number)
99078049779952660735…74729068021557872639
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
9.907 × 10⁹⁸(99-digit number)
99078049779952660735…74729068021557872639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.981 × 10⁹⁹(100-digit number)
19815609955990532147…49458136043115745279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.963 × 10⁹⁹(100-digit number)
39631219911981064294…98916272086231490559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
7.926 × 10⁹⁹(100-digit number)
79262439823962128588…97832544172462981119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.585 × 10¹⁰⁰(101-digit number)
15852487964792425717…95665088344925962239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
3.170 × 10¹⁰⁰(101-digit number)
31704975929584851435…91330176689851924479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
6.340 × 10¹⁰⁰(101-digit number)
63409951859169702870…82660353379703848959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.268 × 10¹⁰¹(102-digit number)
12681990371833940574…65320706759407697919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.536 × 10¹⁰¹(102-digit number)
25363980743667881148…30641413518815395839
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:57,639,793 XPM·at block #6,799,467 · updates every 60s
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