Block #1,143,778

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 7/7/2015, 6:55:08 PM · Difficulty 10.9288 · 5,666,286 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2fbfbb48e104fadc3e72d3161ffd71206594830f081bea69680632e78d39dc14

Height

#1,143,778

Difficulty

10.928766

Transactions

3

Size

3.90 KB

Version

2

Bits

0aedc39c

Nonce

502,765,590

Timestamp

7/7/2015, 6:55:08 PM

Confirmations

5,666,286

Merkle Root

20b8dd34f90b2f044fef3eae814145fe6da9a3efe9ef919d30dcdf55be60e13c
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.

4.920 × 10⁹⁵(96-digit number)
49206360112049336226…41023005615098942719
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
4.920 × 10⁹⁵(96-digit number)
49206360112049336226…41023005615098942719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
9.841 × 10⁹⁵(96-digit number)
98412720224098672453…82046011230197885439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.968 × 10⁹⁶(97-digit number)
19682544044819734490…64092022460395770879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
3.936 × 10⁹⁶(97-digit number)
39365088089639468981…28184044920791541759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
7.873 × 10⁹⁶(97-digit number)
78730176179278937962…56368089841583083519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.574 × 10⁹⁷(98-digit number)
15746035235855787592…12736179683166167039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
3.149 × 10⁹⁷(98-digit number)
31492070471711575185…25472359366332334079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
6.298 × 10⁹⁷(98-digit number)
62984140943423150370…50944718732664668159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.259 × 10⁹⁸(99-digit number)
12596828188684630074…01889437465329336319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
2.519 × 10⁹⁸(99-digit number)
25193656377369260148…03778874930658672639
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:57,724,586 XPM·at block #6,810,063 · updates every 60s
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