Block #201,015

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 10/9/2013, 9:16:30 AM · Difficulty 9.8907 · 6,606,803 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
cd888b0977176ffe3a02a128e790b33004f580be29bcd9762c4c27c253d185ca

Height

#201,015

Difficulty

9.890698

Transactions

1

Size

4.10 KB

Version

2

Bits

09e404c4

Nonce

1,164,856,952

Timestamp

10/9/2013, 9:16:30 AM

Confirmations

6,606,803

Merkle Root

977b545c5f9ad2998c29d11758917a411ec647bddd3239e384b48115c2ef958b
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.

3.291 × 10⁹⁴(95-digit number)
32916790599652093360…00780225857466611519
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
3.291 × 10⁹⁴(95-digit number)
32916790599652093360…00780225857466611519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
6.583 × 10⁹⁴(95-digit number)
65833581199304186720…01560451714933223039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.316 × 10⁹⁵(96-digit number)
13166716239860837344…03120903429866446079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.633 × 10⁹⁵(96-digit number)
26333432479721674688…06241806859732892159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
5.266 × 10⁹⁵(96-digit number)
52666864959443349376…12483613719465784319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.053 × 10⁹⁶(97-digit number)
10533372991888669875…24967227438931568639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.106 × 10⁹⁶(97-digit number)
21066745983777339750…49934454877863137279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
4.213 × 10⁹⁶(97-digit number)
42133491967554679501…99868909755726274559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
8.426 × 10⁹⁶(97-digit number)
84266983935109359002…99737819511452549119
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 consecutive prime numbers forming a Cunningham Chain of the First 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,706,579 XPM·at block #6,807,817 · 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