Block #377,481

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/27/2014, 4:06:03 AM · Difficulty 10.4195 · 6,418,326 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f4821d1b48c20eaf746e74f94c9b9faba91107ab0329451e164aa2a54f415d4f

Height

#377,481

Difficulty

10.419533

Transactions

2

Size

642 B

Version

2

Bits

0a6b668b

Nonce

24,007

Timestamp

1/27/2014, 4:06:03 AM

Confirmations

6,418,326

Merkle Root

885fa044184fa5e4f663df0dd7432fa927d4c45fa7c68576d4e8ab1dcb2a59be
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.

1.311 × 10⁹²(93-digit number)
13113837874440859108…68987294933010489081
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
1.311 × 10⁹²(93-digit number)
13113837874440859108…68987294933010489081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.622 × 10⁹²(93-digit number)
26227675748881718216…37974589866020978161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
5.245 × 10⁹²(93-digit number)
52455351497763436432…75949179732041956321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.049 × 10⁹³(94-digit number)
10491070299552687286…51898359464083912641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.098 × 10⁹³(94-digit number)
20982140599105374573…03796718928167825281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
4.196 × 10⁹³(94-digit number)
41964281198210749146…07593437856335650561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
8.392 × 10⁹³(94-digit number)
83928562396421498292…15186875712671301121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.678 × 10⁹⁴(95-digit number)
16785712479284299658…30373751425342602241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.357 × 10⁹⁴(95-digit number)
33571424958568599317…60747502850685204481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
6.714 × 10⁹⁴(95-digit number)
67142849917137198634…21495005701370408961
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:57,610,535 XPM·at block #6,795,806 · updates every 60s
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