Block #2,656,380

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 5/11/2018, 1:04:54 AM · Difficulty 11.6891 · 4,174,297 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2c2a681f31ef2ae2aae473bd7927386f910e0a5070509ddda8372e6d919fb761

Height

#2,656,380

Difficulty

11.689071

Transactions

2

Size

722 B

Version

2

Bits

0bb066fd

Nonce

522,238,030

Timestamp

5/11/2018, 1:04:54 AM

Confirmations

4,174,297

Merkle Root

60fc1d76775fd68f6954aedea1a003f211b82801b10c648a177348444e83ff40
Transactions (2)
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.

1.158 × 10⁹⁷(98-digit number)
11585525210794337891…12506388237415470081
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
1.158 × 10⁹⁷(98-digit number)
11585525210794337891…12506388237415470081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.317 × 10⁹⁷(98-digit number)
23171050421588675783…25012776474830940161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
4.634 × 10⁹⁷(98-digit number)
46342100843177351567…50025552949661880321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
9.268 × 10⁹⁷(98-digit number)
92684201686354703135…00051105899323760641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.853 × 10⁹⁸(99-digit number)
18536840337270940627…00102211798647521281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.707 × 10⁹⁸(99-digit number)
37073680674541881254…00204423597295042561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
7.414 × 10⁹⁸(99-digit number)
74147361349083762508…00408847194590085121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.482 × 10⁹⁹(100-digit number)
14829472269816752501…00817694389180170241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.965 × 10⁹⁹(100-digit number)
29658944539633505003…01635388778360340481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
5.931 × 10⁹⁹(100-digit number)
59317889079267010006…03270777556720680961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
1.186 × 10¹⁰⁰(101-digit number)
11863577815853402001…06541555113441361921
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:57,889,546 XPM·at block #6,830,676 · 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