Block #1,145,563

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/8/2015, 10:08:31 PM · Difficulty 10.9309 · 5,671,031 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
dd24b214086b5c1deced4e01f02be699fc2f64cc5de141be54df15c4d8e78dd3

Height

#1,145,563

Difficulty

10.930902

Transactions

4

Size

5.04 KB

Version

2

Bits

0aee4f93

Nonce

702,965,177

Timestamp

7/8/2015, 10:08:31 PM

Confirmations

5,671,031

Merkle Root

7e245d286e0dd92de8971b40b3fe89cc0248b59cfb99252312f3a0190d9ab3c3
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.

2.045 × 10⁹⁶(97-digit number)
20451286358364472501…70267453626986210561
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
2.045 × 10⁹⁶(97-digit number)
20451286358364472501…70267453626986210561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
4.090 × 10⁹⁶(97-digit number)
40902572716728945002…40534907253972421121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
8.180 × 10⁹⁶(97-digit number)
81805145433457890005…81069814507944842241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.636 × 10⁹⁷(98-digit number)
16361029086691578001…62139629015889684481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.272 × 10⁹⁷(98-digit number)
32722058173383156002…24279258031779368961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
6.544 × 10⁹⁷(98-digit number)
65444116346766312004…48558516063558737921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.308 × 10⁹⁸(99-digit number)
13088823269353262400…97117032127117475841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.617 × 10⁹⁸(99-digit number)
26177646538706524801…94234064254234951681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
5.235 × 10⁹⁸(99-digit number)
52355293077413049603…88468128508469903361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.047 × 10⁹⁹(100-digit number)
10471058615482609920…76936257016939806721
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:57,776,876 XPM·at block #6,816,593 · updates every 60s
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