Block #2,445,867

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 12/28/2017, 11:07:40 AM · Difficulty 10.9411 · 4,380,858 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
68d54569fc3fba56c3257861c45c777a14f523cfda543e76ddb70d4270fa2696

Height

#2,445,867

Difficulty

10.941134

Transactions

2

Size

869 B

Version

2

Bits

0af0ee2a

Nonce

171,784,303

Timestamp

12/28/2017, 11:07:40 AM

Confirmations

4,380,858

Merkle Root

0dfbd3d641e055bb24209c09c49bbe0151f2cb92a9dc419a2bd85be8b9919727
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.

2.615 × 10⁹³(94-digit number)
26156691524235656803…92933082001543109859
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
2.615 × 10⁹³(94-digit number)
26156691524235656803…92933082001543109859
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
5.231 × 10⁹³(94-digit number)
52313383048471313607…85866164003086219719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.046 × 10⁹⁴(95-digit number)
10462676609694262721…71732328006172439439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.092 × 10⁹⁴(95-digit number)
20925353219388525443…43464656012344878879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
4.185 × 10⁹⁴(95-digit number)
41850706438777050886…86929312024689757759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
8.370 × 10⁹⁴(95-digit number)
83701412877554101772…73858624049379515519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.674 × 10⁹⁵(96-digit number)
16740282575510820354…47717248098759031039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
3.348 × 10⁹⁵(96-digit number)
33480565151021640708…95434496197518062079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
6.696 × 10⁹⁵(96-digit number)
66961130302043281417…90868992395036124159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.339 × 10⁹⁶(97-digit number)
13392226060408656283…81737984790072248319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
2.678 × 10⁹⁶(97-digit number)
26784452120817312567…63475969580144496639
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,857,953 XPM·at block #6,826,724 · updates every 60s
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