Block #370,579

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/22/2014, 6:10:30 AM · Difficulty 10.4376 · 6,445,675 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0f7341ef0786e5cfbb1f8fe8d9478b3118f36fdae6b1a6461c092c51b61d7065

Height

#370,579

Difficulty

10.437586

Transactions

5

Size

1.08 KB

Version

2

Bits

0a70059f

Nonce

238,984

Timestamp

1/22/2014, 6:10:30 AM

Confirmations

6,445,675

Merkle Root

ce4bf2f87017dc4cb1a74fca7fa7e34bac7f6151dc92cf50db9787b9f30a5e13
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.

3.322 × 10⁹³(94-digit number)
33228749332751868486…17688026021938540001
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
3.322 × 10⁹³(94-digit number)
33228749332751868486…17688026021938540001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
6.645 × 10⁹³(94-digit number)
66457498665503736973…35376052043877080001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.329 × 10⁹⁴(95-digit number)
13291499733100747394…70752104087754160001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.658 × 10⁹⁴(95-digit number)
26582999466201494789…41504208175508320001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
5.316 × 10⁹⁴(95-digit number)
53165998932402989578…83008416351016640001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.063 × 10⁹⁵(96-digit number)
10633199786480597915…66016832702033280001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.126 × 10⁹⁵(96-digit number)
21266399572961195831…32033665404066560001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
4.253 × 10⁹⁵(96-digit number)
42532799145922391662…64067330808133120001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
8.506 × 10⁹⁵(96-digit number)
85065598291844783325…28134661616266240001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.701 × 10⁹⁶(97-digit number)
17013119658368956665…56269323232532480001
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:57,774,152 XPM·at block #6,816,253 · updates every 60s
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