Block #1,423,244

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/22/2016, 1:08:29 AM · Difficulty 10.7794 · 5,419,782 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b4df7247630ec529cbd587820c7494dad9883f62c6aa2acfbc0134eb32517b75

Height

#1,423,244

Difficulty

10.779369

Transactions

41

Size

12.80 KB

Version

2

Bits

0ac784c0

Nonce

328,824,537

Timestamp

1/22/2016, 1:08:29 AM

Confirmations

5,419,782

Merkle Root

1f6dbe10dd854d249aa6c8cc28471434b577ee05d40d1dfae3b71c060b7614cc
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.

4.395 × 10⁹⁶(97-digit number)
43958637036854876359…81604744160370933761
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
4.395 × 10⁹⁶(97-digit number)
43958637036854876359…81604744160370933761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
8.791 × 10⁹⁶(97-digit number)
87917274073709752718…63209488320741867521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.758 × 10⁹⁷(98-digit number)
17583454814741950543…26418976641483735041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
3.516 × 10⁹⁷(98-digit number)
35166909629483901087…52837953282967470081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
7.033 × 10⁹⁷(98-digit number)
70333819258967802174…05675906565934940161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.406 × 10⁹⁸(99-digit number)
14066763851793560434…11351813131869880321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.813 × 10⁹⁸(99-digit number)
28133527703587120869…22703626263739760641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
5.626 × 10⁹⁸(99-digit number)
56267055407174241739…45407252527479521281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.125 × 10⁹⁹(100-digit number)
11253411081434848347…90814505054959042561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.250 × 10⁹⁹(100-digit number)
22506822162869696695…81629010109918085121
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:57,988,562 XPM·at block #6,843,025 · updates every 60s
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