Block #2,237,130

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 8/4/2017, 9:09:13 PM · Difficulty 10.9462 · 4,599,726 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2a5dd2687f5839e16a156d604986811d04b8c0ca286c299d31fa376f89bab5ff

Height

#2,237,130

Difficulty

10.946228

Transactions

3

Size

801 B

Version

2

Bits

0af23c01

Nonce

1,749,300,280

Timestamp

8/4/2017, 9:09:13 PM

Confirmations

4,599,726

Merkle Root

8961f3171e2afc061fc0ab592b8f901f9329128a3862493d28c127494b94e009
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.

1.214 × 10⁹⁴(95-digit number)
12147719305518062612…56987997189505347001
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
1.214 × 10⁹⁴(95-digit number)
12147719305518062612…56987997189505347001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.429 × 10⁹⁴(95-digit number)
24295438611036125224…13975994379010694001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
4.859 × 10⁹⁴(95-digit number)
48590877222072250449…27951988758021388001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
9.718 × 10⁹⁴(95-digit number)
97181754444144500899…55903977516042776001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.943 × 10⁹⁵(96-digit number)
19436350888828900179…11807955032085552001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.887 × 10⁹⁵(96-digit number)
38872701777657800359…23615910064171104001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
7.774 × 10⁹⁵(96-digit number)
77745403555315600719…47231820128342208001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.554 × 10⁹⁶(97-digit number)
15549080711063120143…94463640256684416001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.109 × 10⁹⁶(97-digit number)
31098161422126240287…88927280513368832001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
6.219 × 10⁹⁶(97-digit number)
62196322844252480575…77854561026737664001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
1.243 × 10⁹⁷(98-digit number)
12439264568850496115…55709122053475328001
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:57,939,136 XPM·at block #6,836,855 · 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