Block #1,497,122

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/15/2016, 1:05:40 AM · Difficulty 10.6459 · 5,345,341 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6840e0042dc72b01b0adf1aaee391e4b2b0573d9ee54cbe7161fba2419eb7f1d

Height

#1,497,122

Difficulty

10.645864

Transactions

3

Size

4.70 KB

Version

2

Bits

0aa55751

Nonce

2,067,710,411

Timestamp

3/15/2016, 1:05:40 AM

Confirmations

5,345,341

Merkle Root

e053368d66e1a972a09c192834f5b497d35866e03ad38d60a862b2b9da759700
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.

1.714 × 10⁹⁴(95-digit number)
17145022955438833213…96765283187601036121
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
1.714 × 10⁹⁴(95-digit number)
17145022955438833213…96765283187601036121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
3.429 × 10⁹⁴(95-digit number)
34290045910877666426…93530566375202072241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
6.858 × 10⁹⁴(95-digit number)
68580091821755332853…87061132750404144481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.371 × 10⁹⁵(96-digit number)
13716018364351066570…74122265500808288961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.743 × 10⁹⁵(96-digit number)
27432036728702133141…48244531001616577921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
5.486 × 10⁹⁵(96-digit number)
54864073457404266282…96489062003233155841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.097 × 10⁹⁶(97-digit number)
10972814691480853256…92978124006466311681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.194 × 10⁹⁶(97-digit number)
21945629382961706513…85956248012932623361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
4.389 × 10⁹⁶(97-digit number)
43891258765923413026…71912496025865246721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
8.778 × 10⁹⁶(97-digit number)
87782517531846826052…43824992051730493441
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:57,984,122 XPM·at block #6,842,462 · 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