Block #1,170,352

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 7/25/2015, 10:19:53 PM · Difficulty 10.9357 · 5,644,792 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0b36277c3bfe7a3946cba9d423588fee8e0fab14af2ccb7691aeb1c6b833d5a1

Height

#1,170,352

Difficulty

10.935704

Transactions

4

Size

1.15 KB

Version

2

Bits

0aef8a54

Nonce

390,694,491

Timestamp

7/25/2015, 10:19:53 PM

Confirmations

5,644,792

Merkle Root

32dd085e36c7463025638c572fd372e619a1e9ea1c20de12a39e0c6ef4cdd30a
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.

4.557 × 10⁹³(94-digit number)
45570342895582359332…71273149222808597281
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
4.557 × 10⁹³(94-digit number)
45570342895582359332…71273149222808597281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
9.114 × 10⁹³(94-digit number)
91140685791164718665…42546298445617194561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.822 × 10⁹⁴(95-digit number)
18228137158232943733…85092596891234389121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
3.645 × 10⁹⁴(95-digit number)
36456274316465887466…70185193782468778241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
7.291 × 10⁹⁴(95-digit number)
72912548632931774932…40370387564937556481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.458 × 10⁹⁵(96-digit number)
14582509726586354986…80740775129875112961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.916 × 10⁹⁵(96-digit number)
29165019453172709972…61481550259750225921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
5.833 × 10⁹⁵(96-digit number)
58330038906345419945…22963100519500451841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.166 × 10⁹⁶(97-digit number)
11666007781269083989…45926201039000903681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.333 × 10⁹⁶(97-digit number)
23332015562538167978…91852402078001807361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
4.666 × 10⁹⁶(97-digit number)
46664031125076335956…83704804156003614721
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,765,246 XPM·at block #6,815,143 · 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.
Privacy Policy·

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