Block #1,569,372

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 5/2/2016, 10:37:38 PM · Difficulty 10.7564 · 5,240,378 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
12cb055c63e80054db5e6fac6513bc9f858d8e17b236ad9281ecd6186efdd5a4

Height

#1,569,372

Difficulty

10.756382

Transactions

3

Size

3.89 KB

Version

2

Bits

0ac1a239

Nonce

239,102,416

Timestamp

5/2/2016, 10:37:38 PM

Confirmations

5,240,378

Merkle Root

192e81d966d573f0855a397a459e360cb133fcf3d2c368306e02d83494b4d848
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.

6.062 × 10⁹²(93-digit number)
60621889205199283575…42344239365134670799
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
6.062 × 10⁹²(93-digit number)
60621889205199283575…42344239365134670799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.212 × 10⁹³(94-digit number)
12124377841039856715…84688478730269341599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.424 × 10⁹³(94-digit number)
24248755682079713430…69376957460538683199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
4.849 × 10⁹³(94-digit number)
48497511364159426860…38753914921077366399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
9.699 × 10⁹³(94-digit number)
96995022728318853721…77507829842154732799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.939 × 10⁹⁴(95-digit number)
19399004545663770744…55015659684309465599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
3.879 × 10⁹⁴(95-digit number)
38798009091327541488…10031319368618931199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
7.759 × 10⁹⁴(95-digit number)
77596018182655082976…20062638737237862399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.551 × 10⁹⁵(96-digit number)
15519203636531016595…40125277474475724799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
3.103 × 10⁹⁵(96-digit number)
31038407273062033190…80250554948951449599
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,722,085 XPM·at block #6,809,749 · updates every 60s
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