Block #1,441,230

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/3/2016, 7:03:55 PM · Difficulty 10.7633 · 5,386,173 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
44d60f0d61d3cf76245ef96a549c4cbdea78e5f7af0156d704ed8f07e6193ac2

Height

#1,441,230

Difficulty

10.763333

Transactions

3

Size

2.49 KB

Version

2

Bits

0ac369cf

Nonce

131,007,426

Timestamp

2/3/2016, 7:03:55 PM

Confirmations

5,386,173

Merkle Root

f874be81bd1a71fd810ec7162e3eec8c336c70edc7663c76209bb6569e76dde5
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.

2.439 × 10⁹⁴(95-digit number)
24394621888579067733…17311384393582700761
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
2.439 × 10⁹⁴(95-digit number)
24394621888579067733…17311384393582700761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
4.878 × 10⁹⁴(95-digit number)
48789243777158135466…34622768787165401521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
9.757 × 10⁹⁴(95-digit number)
97578487554316270933…69245537574330803041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.951 × 10⁹⁵(96-digit number)
19515697510863254186…38491075148661606081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.903 × 10⁹⁵(96-digit number)
39031395021726508373…76982150297323212161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
7.806 × 10⁹⁵(96-digit number)
78062790043453016746…53964300594646424321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.561 × 10⁹⁶(97-digit number)
15612558008690603349…07928601189292848641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.122 × 10⁹⁶(97-digit number)
31225116017381206698…15857202378585697281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
6.245 × 10⁹⁶(97-digit number)
62450232034762413397…31714404757171394561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.249 × 10⁹⁷(98-digit number)
12490046406952482679…63428809514342789121
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:57,863,329 XPM·at block #6,827,402 · updates every 60s
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