Block #106,606

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 8/9/2013, 2:48:49 AM · Difficulty 9.6104 · 6,706,370 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
58e20a1157b1a84bf5af1dbbcd613226912c6a93ca026d38ad2412ec7b5dc3ea

Height

#106,606

Difficulty

9.610444

Transactions

2

Size

428 B

Version

2

Bits

099c4614

Nonce

59,273

Timestamp

8/9/2013, 2:48:49 AM

Confirmations

6,706,370

Merkle Root

941d55e0087c86e6a1d861c42fadbb7ddfff77a1978c1008317e60e8e06095a2
Transactions (2)
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.

8.006 × 10⁹⁹(100-digit number)
80063938571982362883…29189551934179574239
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
8.006 × 10⁹⁹(100-digit number)
80063938571982362883…29189551934179574239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.601 × 10¹⁰⁰(101-digit number)
16012787714396472576…58379103868359148479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.202 × 10¹⁰⁰(101-digit number)
32025575428792945153…16758207736718296959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
6.405 × 10¹⁰⁰(101-digit number)
64051150857585890307…33516415473436593919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.281 × 10¹⁰¹(102-digit number)
12810230171517178061…67032830946873187839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.562 × 10¹⁰¹(102-digit number)
25620460343034356122…34065661893746375679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
5.124 × 10¹⁰¹(102-digit number)
51240920686068712245…68131323787492751359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.024 × 10¹⁰²(103-digit number)
10248184137213742449…36262647574985502719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.049 × 10¹⁰²(103-digit number)
20496368274427484898…72525295149971005439
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:57,747,852 XPM·at block #6,812,975 · updates every 60s
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