1. #6,808,744TWN11 primes

    Bi-Twin · ⛏️ coinsforall.io

Block #239,801

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 11/2/2013, 7:46:02 AM · Difficulty 9.9548 · 6,568,944 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e4ba4ec96380c07920c31ec5f103d9648d1a1f581cb6be9c62f5be06e66a3a0a

Height

#239,801

Difficulty

9.954845

Transactions

3

Size

945 B

Version

2

Bits

09f470ba

Nonce

18,398

Timestamp

11/2/2013, 7:46:02 AM

Confirmations

6,568,944

Merkle Root

78c9054e6f80f452e3fd40705d9819b834d06584d1987217c7361005862856a8
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.

1.517 × 10⁹³(94-digit number)
15171006961038582908…59651788898836541439
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
1.517 × 10⁹³(94-digit number)
15171006961038582908…59651788898836541439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
3.034 × 10⁹³(94-digit number)
30342013922077165816…19303577797673082879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
6.068 × 10⁹³(94-digit number)
60684027844154331633…38607155595346165759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.213 × 10⁹⁴(95-digit number)
12136805568830866326…77214311190692331519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.427 × 10⁹⁴(95-digit number)
24273611137661732653…54428622381384663039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
4.854 × 10⁹⁴(95-digit number)
48547222275323465306…08857244762769326079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
9.709 × 10⁹⁴(95-digit number)
97094444550646930613…17714489525538652159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.941 × 10⁹⁵(96-digit number)
19418888910129386122…35428979051077304319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
3.883 × 10⁹⁵(96-digit number)
38837777820258772245…70857958102154608639
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:57,714,008 XPM·at block #6,808,744 · 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