Block #390,460

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/5/2014, 4:34:24 AM · Difficulty 10.4231 · 6,417,928 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4db786d9006e9ed5fb300f87d30e2513fc4f36229ecf050a5080ef21447c943b

Height

#390,460

Difficulty

10.423110

Transactions

1

Size

901 B

Version

2

Bits

0a6c50f4

Nonce

159,234

Timestamp

2/5/2014, 4:34:24 AM

Confirmations

6,417,928

Merkle Root

5fc3b4a1150635cca4572e00e21cb355433cfe4fe99aabbc2053c872925510fe
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.

3.126 × 10⁹⁵(96-digit number)
31264736154140421696…25561064217669463041
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
3.126 × 10⁹⁵(96-digit number)
31264736154140421696…25561064217669463041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
6.252 × 10⁹⁵(96-digit number)
62529472308280843392…51122128435338926081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.250 × 10⁹⁶(97-digit number)
12505894461656168678…02244256870677852161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.501 × 10⁹⁶(97-digit number)
25011788923312337356…04488513741355704321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
5.002 × 10⁹⁶(97-digit number)
50023577846624674713…08977027482711408641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.000 × 10⁹⁷(98-digit number)
10004715569324934942…17954054965422817281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.000 × 10⁹⁷(98-digit number)
20009431138649869885…35908109930845634561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
4.001 × 10⁹⁷(98-digit number)
40018862277299739770…71816219861691269121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
8.003 × 10⁹⁷(98-digit number)
80037724554599479541…43632439723382538241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.600 × 10⁹⁸(99-digit number)
16007544910919895908…87264879446765076481
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:57,711,159 XPM·at block #6,808,387 · updates every 60s
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