Block #1,106,215

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 6/15/2015, 8:18:58 AM · Difficulty 10.7950 · 5,702,127 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a2cbea3b5cd24c74955db47da9edf2c19b4d45626fe289d465666e016556aa63

Height

#1,106,215

Difficulty

10.794990

Transactions

5

Size

7.26 KB

Version

2

Bits

0acb847d

Nonce

236,505,574

Timestamp

6/15/2015, 8:18:58 AM

Confirmations

5,702,127

Merkle Root

9b58dde8846a95313ca78a02c1c3c4c039e2237c011b8af3d129cfed2b0c44e7
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.

6.516 × 10⁹⁵(96-digit number)
65167821397610812463…94258455757244730241
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
6.516 × 10⁹⁵(96-digit number)
65167821397610812463…94258455757244730241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.303 × 10⁹⁶(97-digit number)
13033564279522162492…88516911514489460481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.606 × 10⁹⁶(97-digit number)
26067128559044324985…77033823028978920961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
5.213 × 10⁹⁶(97-digit number)
52134257118088649970…54067646057957841921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.042 × 10⁹⁷(98-digit number)
10426851423617729994…08135292115915683841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.085 × 10⁹⁷(98-digit number)
20853702847235459988…16270584231831367681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
4.170 × 10⁹⁷(98-digit number)
41707405694470919976…32541168463662735361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
8.341 × 10⁹⁷(98-digit number)
83414811388941839952…65082336927325470721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.668 × 10⁹⁸(99-digit number)
16682962277788367990…30164673854650941441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.336 × 10⁹⁸(99-digit number)
33365924555576735981…60329347709301882881
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:57,710,793 XPM·at block #6,808,341 · 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