Block #374,812

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/25/2014, 7:41:20 AM · Difficulty 10.4186 · 6,441,630 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
9389fa84cc2255c56e1e787c57e6932f52f95bb9ce260ffd6409d30a7d66c11c

Height

#374,812

Difficulty

10.418589

Transactions

3

Size

650 B

Version

2

Bits

0a6b289f

Nonce

171,048

Timestamp

1/25/2014, 7:41:20 AM

Confirmations

6,441,630

Merkle Root

95b7ed6806b8590d4b38e8620c4ccbb0837e485af938497d200a558d43896e82
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.

5.984 × 10⁹¹(92-digit number)
59846232672966938840…94301522827326289531
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
5.984 × 10⁹¹(92-digit number)
59846232672966938840…94301522827326289531
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.196 × 10⁹²(93-digit number)
11969246534593387768…88603045654652579061
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.393 × 10⁹²(93-digit number)
23938493069186775536…77206091309305158121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
4.787 × 10⁹²(93-digit number)
47876986138373551072…54412182618610316241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
9.575 × 10⁹²(93-digit number)
95753972276747102144…08824365237220632481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.915 × 10⁹³(94-digit number)
19150794455349420428…17648730474441264961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.830 × 10⁹³(94-digit number)
38301588910698840857…35297460948882529921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
7.660 × 10⁹³(94-digit number)
76603177821397681715…70594921897765059841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.532 × 10⁹⁴(95-digit number)
15320635564279536343…41189843795530119681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.064 × 10⁹⁴(95-digit number)
30641271128559072686…82379687591060239361
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:57,775,662 XPM·at block #6,816,441 · updates every 60s
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