Block #1,066,690

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 5/19/2015, 5:55:33 PM · Difficulty 10.7374 · 5,742,894 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f14a75a6ba65b1a3a5bb6772b4b0ef490f47776e2a3f8c3b509a28fad5565278

Height

#1,066,690

Difficulty

10.737408

Transactions

3

Size

659 B

Version

2

Bits

0abcc6c2

Nonce

11,291,384

Timestamp

5/19/2015, 5:55:33 PM

Confirmations

5,742,894

Merkle Root

6080d2a96a12e7e90e9064e5c86f9976524752cde953e5ad63ab06224908495f
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.

1.461 × 10⁹⁷(98-digit number)
14611164458951887766…59193660448133560321
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
1.461 × 10⁹⁷(98-digit number)
14611164458951887766…59193660448133560321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.922 × 10⁹⁷(98-digit number)
29222328917903775533…18387320896267120641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
5.844 × 10⁹⁷(98-digit number)
58444657835807551066…36774641792534241281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.168 × 10⁹⁸(99-digit number)
11688931567161510213…73549283585068482561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.337 × 10⁹⁸(99-digit number)
23377863134323020426…47098567170136965121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
4.675 × 10⁹⁸(99-digit number)
46755726268646040853…94197134340273930241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
9.351 × 10⁹⁸(99-digit number)
93511452537292081706…88394268680547860481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.870 × 10⁹⁹(100-digit number)
18702290507458416341…76788537361095720961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.740 × 10⁹⁹(100-digit number)
37404581014916832682…53577074722191441921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
7.480 × 10⁹⁹(100-digit number)
74809162029833665364…07154149444382883841
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:57,720,750 XPM·at block #6,809,583 · updates every 60s
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