Block #108,697

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 8/10/2013, 3:30:12 AM · Difficulty 9.6549 · 6,708,112 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
40598e98dbad796ec05559ce36bf1875bdd5690e0889087aedc007df29c42b5b

Height

#108,697

Difficulty

9.654863

Transactions

2

Size

360 B

Version

2

Bits

09a7a51c

Nonce

6,741

Timestamp

8/10/2013, 3:30:12 AM

Confirmations

6,708,112

Merkle Root

5570ebca8c3e83a63936dac560dd080145f813aa5f659e4a6554b49b5db1d0f8
Transactions (2)
1 in → 1 out10.7200 XPM109 B
1 in → 1 out10.8600 XPM159 B
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.

4.270 × 10⁹⁹(100-digit number)
42701022598263884876…19580170298888256161
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
4.270 × 10⁹⁹(100-digit number)
42701022598263884876…19580170298888256161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
8.540 × 10⁹⁹(100-digit number)
85402045196527769752…39160340597776512321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.708 × 10¹⁰⁰(101-digit number)
17080409039305553950…78320681195553024641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
3.416 × 10¹⁰⁰(101-digit number)
34160818078611107901…56641362391106049281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
6.832 × 10¹⁰⁰(101-digit number)
68321636157222215802…13282724782212098561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.366 × 10¹⁰¹(102-digit number)
13664327231444443160…26565449564424197121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.732 × 10¹⁰¹(102-digit number)
27328654462888886320…53130899128848394241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
5.465 × 10¹⁰¹(102-digit number)
54657308925777772641…06261798257696788481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.093 × 10¹⁰²(103-digit number)
10931461785155554528…12523596515393576961
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 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
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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …
Circulating Supply:57,778,509 XPM·at block #6,816,808 · 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