Block #447,385

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/17/2014, 6:24:39 AM · Difficulty 10.3546 · 6,362,423 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f9b9ba16323f0621628efa40388060f041f01564cfbd625471cdde32e0179956

Height

#447,385

Difficulty

10.354627

Transactions

1

Size

935 B

Version

2

Bits

0a5ac8d2

Nonce

395,654

Timestamp

3/17/2014, 6:24:39 AM

Confirmations

6,362,423

Merkle Root

0a3f8f5c588621af0f84e4ad2bb1d6364364c891ab3c3094f358f4e60f110b6a
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.

6.418 × 10⁹⁴(95-digit number)
64180308769572624059…32957831767338848001
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
6.418 × 10⁹⁴(95-digit number)
64180308769572624059…32957831767338848001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.283 × 10⁹⁵(96-digit number)
12836061753914524811…65915663534677696001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.567 × 10⁹⁵(96-digit number)
25672123507829049623…31831327069355392001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
5.134 × 10⁹⁵(96-digit number)
51344247015658099247…63662654138710784001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.026 × 10⁹⁶(97-digit number)
10268849403131619849…27325308277421568001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.053 × 10⁹⁶(97-digit number)
20537698806263239699…54650616554843136001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
4.107 × 10⁹⁶(97-digit number)
41075397612526479398…09301233109686272001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
8.215 × 10⁹⁶(97-digit number)
82150795225052958796…18602466219372544001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.643 × 10⁹⁷(98-digit number)
16430159045010591759…37204932438745088001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.286 × 10⁹⁷(98-digit number)
32860318090021183518…74409864877490176001
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:57,722,546 XPM·at block #6,809,807 · updates every 60s
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