Block #1,180,982

2CCLength 12★★★★☆

Cunningham Chain of the Second Kind · Discovered 8/2/2015, 11:06:27 PM · Difficulty 10.9230 · 5,625,280 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
478d1462341023c4fd9a8716154a1d63594f93a81bb7b4656a5cd3ee54cc1cba

Height

#1,180,982

Difficulty

10.922971

Transactions

4

Size

3.38 KB

Version

2

Bits

0aec47ce

Nonce

444,880,517

Timestamp

8/2/2015, 11:06:27 PM

Confirmations

5,625,280

Merkle Root

13a478d1f34c3a1d527dd5eba8365487828bd776fcdfb997734aec0ebd2dfe1a
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.

5.240 × 10⁹⁶(97-digit number)
52405937117627775197…24005012963450435841
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
5.240 × 10⁹⁶(97-digit number)
52405937117627775197…24005012963450435841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.048 × 10⁹⁷(98-digit number)
10481187423525555039…48010025926900871681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.096 × 10⁹⁷(98-digit number)
20962374847051110078…96020051853801743361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
4.192 × 10⁹⁷(98-digit number)
41924749694102220157…92040103707603486721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
8.384 × 10⁹⁷(98-digit number)
83849499388204440315…84080207415206973441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.676 × 10⁹⁸(99-digit number)
16769899877640888063…68160414830413946881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.353 × 10⁹⁸(99-digit number)
33539799755281776126…36320829660827893761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
6.707 × 10⁹⁸(99-digit number)
67079599510563552252…72641659321655787521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.341 × 10⁹⁹(100-digit number)
13415919902112710450…45283318643311575041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.683 × 10⁹⁹(100-digit number)
26831839804225420901…90566637286623150081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
5.366 × 10⁹⁹(100-digit number)
53663679608450841802…81133274573246300161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
12
2^11 × origin + 1
1.073 × 10¹⁰⁰(101-digit number)
10732735921690168360…62266549146492600321
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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:57,694,180 XPM·at block #6,806,261 · updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

·Privacy Policy