Block #1,390,322

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/29/2015, 4:12:05 PM · Difficulty 10.8082 · 5,436,834 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
aab3168649435a7a7618fd96254c900550d874cc738e5b42e25aa1f047349c2d

Height

#1,390,322

Difficulty

10.808241

Transactions

2

Size

1.11 KB

Version

2

Bits

0acee8e1

Nonce

340,704,587

Timestamp

12/29/2015, 4:12:05 PM

Confirmations

5,436,834

Merkle Root

9ef8290b11225f030b3c344de6dd57bf7851cab4197a9765d7e3677a9f77166f
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.

1.723 × 10⁹⁷(98-digit number)
17231201185263903914…51786604951621043201
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
1.723 × 10⁹⁷(98-digit number)
17231201185263903914…51786604951621043201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
3.446 × 10⁹⁷(98-digit number)
34462402370527807828…03573209903242086401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
6.892 × 10⁹⁷(98-digit number)
68924804741055615657…07146419806484172801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.378 × 10⁹⁸(99-digit number)
13784960948211123131…14292839612968345601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.756 × 10⁹⁸(99-digit number)
27569921896422246263…28585679225936691201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
5.513 × 10⁹⁸(99-digit number)
55139843792844492526…57171358451873382401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.102 × 10⁹⁹(100-digit number)
11027968758568898505…14342716903746764801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.205 × 10⁹⁹(100-digit number)
22055937517137797010…28685433807493529601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
4.411 × 10⁹⁹(100-digit number)
44111875034275594020…57370867614987059201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
8.822 × 10⁹⁹(100-digit number)
88223750068551188041…14741735229974118401
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:57,861,432 XPM·at block #6,827,155 · updates every 60s
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