Block #477,377

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/6/2014, 10:31:34 AM · Difficulty 10.4809 · 6,326,063 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
35e00d1b31c112bfba270eb9d6fc5d37daa6364d351d4ca5ad5965c92b0a67cc

Height

#477,377

Difficulty

10.480886

Transactions

1

Size

1005 B

Version

2

Bits

0a7b1b60

Nonce

88,849

Timestamp

4/6/2014, 10:31:34 AM

Confirmations

6,326,063

Merkle Root

7870c186e83ad3329dcafd3b5a89b34f288d7fe2bdfa2d68b514202a697aaf4c
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.

3.534 × 10⁹⁸(99-digit number)
35349735404115848484…33579892899670649601
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
3.534 × 10⁹⁸(99-digit number)
35349735404115848484…33579892899670649601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
7.069 × 10⁹⁸(99-digit number)
70699470808231696969…67159785799341299201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.413 × 10⁹⁹(100-digit number)
14139894161646339393…34319571598682598401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.827 × 10⁹⁹(100-digit number)
28279788323292678787…68639143197365196801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
5.655 × 10⁹⁹(100-digit number)
56559576646585357575…37278286394730393601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.131 × 10¹⁰⁰(101-digit number)
11311915329317071515…74556572789460787201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.262 × 10¹⁰⁰(101-digit number)
22623830658634143030…49113145578921574401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
4.524 × 10¹⁰⁰(101-digit number)
45247661317268286060…98226291157843148801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
9.049 × 10¹⁰⁰(101-digit number)
90495322634536572121…96452582315686297601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.809 × 10¹⁰¹(102-digit number)
18099064526907314424…92905164631372595201
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 Second 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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …
Circulating Supply:57,671,545 XPM·at block #6,803,439 · updates every 60s
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