Block #379,673

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/28/2014, 4:45:33 PM · Difficulty 10.4193 · 6,429,981 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
093af3846188a6be6a19f3023f43a98e86864ab394c2ae63fa5220ecece8d73c

Height

#379,673

Difficulty

10.419344

Transactions

3

Size

655 B

Version

2

Bits

0a6b5a26

Nonce

133,943

Timestamp

1/28/2014, 4:45:33 PM

Confirmations

6,429,981

Merkle Root

ba5b2af7d1b5bbeca9dce09aba2874ca3eab3374643ca07f08c2c026a801855a
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.

3.834 × 10¹⁰⁰(101-digit number)
38344464676726015545…19932998330235220479
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
3.834 × 10¹⁰⁰(101-digit number)
38344464676726015545…19932998330235220479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
7.668 × 10¹⁰⁰(101-digit number)
76688929353452031090…39865996660470440959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.533 × 10¹⁰¹(102-digit number)
15337785870690406218…79731993320940881919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
3.067 × 10¹⁰¹(102-digit number)
30675571741380812436…59463986641881763839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
6.135 × 10¹⁰¹(102-digit number)
61351143482761624872…18927973283763527679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.227 × 10¹⁰²(103-digit number)
12270228696552324974…37855946567527055359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.454 × 10¹⁰²(103-digit number)
24540457393104649949…75711893135054110719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
4.908 × 10¹⁰²(103-digit number)
49080914786209299898…51423786270108221439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
9.816 × 10¹⁰²(103-digit number)
98161829572418599796…02847572540216442879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.963 × 10¹⁰³(104-digit number)
19632365914483719959…05695145080432885759
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:57,721,313 XPM·at block #6,809,653 · updates every 60s
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