Block #377,383

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/27/2014, 2:09:09 AM · Difficulty 10.4217 · 6,459,246 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
cd745117a515b92adea2bb025773daca89c026f5f989969187f499959de232eb

Height

#377,383

Difficulty

10.421695

Transactions

2

Size

585 B

Version

2

Bits

0a6bf431

Nonce

62,633

Timestamp

1/27/2014, 2:09:09 AM

Confirmations

6,459,246

Merkle Root

b071b9f5bdbce9b31631894b0901fd060d24535d5573d20c2b564cca09257dc1
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.

2.053 × 10¹⁰⁷(108-digit number)
20535793443947567638…68199960656958423039
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
2.053 × 10¹⁰⁷(108-digit number)
20535793443947567638…68199960656958423039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
4.107 × 10¹⁰⁷(108-digit number)
41071586887895135276…36399921313916846079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
8.214 × 10¹⁰⁷(108-digit number)
82143173775790270553…72799842627833692159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.642 × 10¹⁰⁸(109-digit number)
16428634755158054110…45599685255667384319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
3.285 × 10¹⁰⁸(109-digit number)
32857269510316108221…91199370511334768639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
6.571 × 10¹⁰⁸(109-digit number)
65714539020632216443…82398741022669537279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.314 × 10¹⁰⁹(110-digit number)
13142907804126443288…64797482045339074559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.628 × 10¹⁰⁹(110-digit number)
26285815608252886577…29594964090678149119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
5.257 × 10¹⁰⁹(110-digit number)
52571631216505773154…59189928181356298239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.051 × 10¹¹⁰(111-digit number)
10514326243301154630…18379856362712596479
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:57,937,304 XPM·at block #6,836,628 · updates every 60s
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