Block #949,303

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 2/23/2015, 7:27:31 PM · Difficulty 10.8990 · 5,877,882 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
03a6eb23765af4e90645678f0dd1d3f9ff997f34c36d7d3398cc1a0a14ff1036

Height

#949,303

Difficulty

10.898989

Transactions

3

Size

953 B

Version

2

Bits

0ae62423

Nonce

149,273,530

Timestamp

2/23/2015, 7:27:31 PM

Confirmations

5,877,882

Merkle Root

3deb289aaebf20536619fd9baf68d3f9e376a3a04808fe557aa462bb2a125bb4
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.

2.115 × 10⁹⁷(98-digit number)
21155675966444755360…97741425562310830079
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
2.115 × 10⁹⁷(98-digit number)
21155675966444755360…97741425562310830079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
4.231 × 10⁹⁷(98-digit number)
42311351932889510721…95482851124621660159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
8.462 × 10⁹⁷(98-digit number)
84622703865779021442…90965702249243320319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.692 × 10⁹⁸(99-digit number)
16924540773155804288…81931404498486640639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
3.384 × 10⁹⁸(99-digit number)
33849081546311608577…63862808996973281279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
6.769 × 10⁹⁸(99-digit number)
67698163092623217154…27725617993946562559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.353 × 10⁹⁹(100-digit number)
13539632618524643430…55451235987893125119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.707 × 10⁹⁹(100-digit number)
27079265237049286861…10902471975786250239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
5.415 × 10⁹⁹(100-digit number)
54158530474098573723…21804943951572500479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.083 × 10¹⁰⁰(101-digit number)
10831706094819714744…43609887903145000959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
2.166 × 10¹⁰⁰(101-digit number)
21663412189639429489…87219775806290001919
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 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
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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,861,576 XPM·at block #6,827,184 · 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