Block #379,220

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/28/2014, 9:34:55 AM · Difficulty 10.4169 · 6,431,184 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7e5de6050e8fa36ac30107650e22f1ec45b7c6be8e5914605b8f0c48f8442a6e

Height

#379,220

Difficulty

10.416920

Transactions

1

Size

833 B

Version

2

Bits

0a6abb3d

Nonce

618,357

Timestamp

1/28/2014, 9:34:55 AM

Confirmations

6,431,184

Merkle Root

01eedacabb6dd9b194831fa1f0eaf976f3525a5e8fa7351b58b8eb551f04d8ca
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.

1.708 × 10⁹⁴(95-digit number)
17086104770772890684…08715203683223341279
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
1.708 × 10⁹⁴(95-digit number)
17086104770772890684…08715203683223341279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
3.417 × 10⁹⁴(95-digit number)
34172209541545781369…17430407366446682559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
6.834 × 10⁹⁴(95-digit number)
68344419083091562738…34860814732893365119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.366 × 10⁹⁵(96-digit number)
13668883816618312547…69721629465786730239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.733 × 10⁹⁵(96-digit number)
27337767633236625095…39443258931573460479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
5.467 × 10⁹⁵(96-digit number)
54675535266473250191…78886517863146920959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.093 × 10⁹⁶(97-digit number)
10935107053294650038…57773035726293841919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.187 × 10⁹⁶(97-digit number)
21870214106589300076…15546071452587683839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
4.374 × 10⁹⁶(97-digit number)
43740428213178600152…31092142905175367679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
8.748 × 10⁹⁶(97-digit number)
87480856426357200305…62184285810350735359
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:57,727,310 XPM·at block #6,810,403 · updates every 60s
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