Block #196,195

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 10/6/2013, 8:13:24 AM · Difficulty 9.8804 · 6,614,126 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f07cc55aaef5c61156b5c0db926550b2e627a62f7ef4aa9fb399699fff26e8e8

Height

#196,195

Difficulty

9.880401

Transactions

1

Size

3.90 KB

Version

2

Bits

09e161f1

Nonce

1,164,776,170

Timestamp

10/6/2013, 8:13:24 AM

Confirmations

6,614,126

Merkle Root

923758f44ccfca83b59e97a361816fb8d276a8a1712e795b0f99e73d1451e3b9
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.

9.943 × 10⁹²(93-digit number)
99433769434614413721…98335642366675737599
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
9.943 × 10⁹²(93-digit number)
99433769434614413721…98335642366675737599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.988 × 10⁹³(94-digit number)
19886753886922882744…96671284733351475199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.977 × 10⁹³(94-digit number)
39773507773845765488…93342569466702950399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
7.954 × 10⁹³(94-digit number)
79547015547691530977…86685138933405900799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.590 × 10⁹⁴(95-digit number)
15909403109538306195…73370277866811801599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
3.181 × 10⁹⁴(95-digit number)
31818806219076612390…46740555733623603199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
6.363 × 10⁹⁴(95-digit number)
63637612438153224781…93481111467247206399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.272 × 10⁹⁵(96-digit number)
12727522487630644956…86962222934494412799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.545 × 10⁹⁵(96-digit number)
25455044975261289912…73924445868988825599
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:57,726,646 XPM·at block #6,810,320 · 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.

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

·Privacy Policy