Block #379,550

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/28/2014, 2:40:55 PM · Difficulty 10.4194 · 6,434,768 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c39272b124a1827b1345ea986e1adb651aa8a579b133589d4763cd5f2cee22e7

Height

#379,550

Difficulty

10.419358

Transactions

4

Size

847 B

Version

2

Bits

0a6b5b04

Nonce

44,759

Timestamp

1/28/2014, 2:40:55 PM

Confirmations

6,434,768

Merkle Root

b8d2947ef6682a3b27b1cda7a7839a80b3b150d0811063a55398dd89a47de6f8
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.

1.413 × 10¹⁰⁰(101-digit number)
14134901237144861777…03723125813685670399
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
1.413 × 10¹⁰⁰(101-digit number)
14134901237144861777…03723125813685670399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.826 × 10¹⁰⁰(101-digit number)
28269802474289723555…07446251627371340799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
5.653 × 10¹⁰⁰(101-digit number)
56539604948579447111…14892503254742681599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.130 × 10¹⁰¹(102-digit number)
11307920989715889422…29785006509485363199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.261 × 10¹⁰¹(102-digit number)
22615841979431778844…59570013018970726399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
4.523 × 10¹⁰¹(102-digit number)
45231683958863557689…19140026037941452799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
9.046 × 10¹⁰¹(102-digit number)
90463367917727115378…38280052075882905599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.809 × 10¹⁰²(103-digit number)
18092673583545423075…76560104151765811199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
3.618 × 10¹⁰²(103-digit number)
36185347167090846151…53120208303531622399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
7.237 × 10¹⁰²(103-digit number)
72370694334181692302…06240416607063244799
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:57,758,608 XPM·at block #6,814,317 · updates every 60s
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