Block #378,719

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/28/2014, 1:37:24 AM · Difficulty 10.4141 · 6,430,866 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
939d3bef2fa4a76da1492428dbef0645215bbe87dbaa53eeb0f346d3ea98aafa

Height

#378,719

Difficulty

10.414083

Transactions

3

Size

950 B

Version

2

Bits

0a6a0159

Nonce

705,944

Timestamp

1/28/2014, 1:37:24 AM

Confirmations

6,430,866

Merkle Root

da2fcdb4af7427ba4c5a352669953b714188f119b273c551b72eec1d4ba3da40
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.

5.265 × 10¹⁰⁰(101-digit number)
52655441958598468381…49515072950549501439
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
5.265 × 10¹⁰⁰(101-digit number)
52655441958598468381…49515072950549501439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.053 × 10¹⁰¹(102-digit number)
10531088391719693676…99030145901099002879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.106 × 10¹⁰¹(102-digit number)
21062176783439387352…98060291802198005759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
4.212 × 10¹⁰¹(102-digit number)
42124353566878774705…96120583604396011519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
8.424 × 10¹⁰¹(102-digit number)
84248707133757549410…92241167208792023039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.684 × 10¹⁰²(103-digit number)
16849741426751509882…84482334417584046079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
3.369 × 10¹⁰²(103-digit number)
33699482853503019764…68964668835168092159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
6.739 × 10¹⁰²(103-digit number)
67398965707006039528…37929337670336184319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.347 × 10¹⁰³(104-digit number)
13479793141401207905…75858675340672368639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
2.695 × 10¹⁰³(104-digit number)
26959586282802415811…51717350681344737279
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:57,720,758 XPM·at block #6,809,584 · updates every 60s
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