Block #2,760,101

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 7/22/2018, 10:34:45 AM · Difficulty 11.6582 · 4,073,612 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2ed1c6634adcb5a5f7178556dfb2b2946ebbfd76ae4cb7703944c50143158174

Height

#2,760,101

Difficulty

11.658197

Transactions

6

Size

2.00 KB

Version

2

Bits

0ba87f99

Nonce

1,896,618,275

Timestamp

7/22/2018, 10:34:45 AM

Confirmations

4,073,612

Merkle Root

d4d836d518bcd54e90ea72fb14bd5b2b30d2a3bb1b10b719b1fda8d46048ca1b
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.

3.869 × 10⁹³(94-digit number)
38692989466755829621…26112745762318638751
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
3.869 × 10⁹³(94-digit number)
38692989466755829621…26112745762318638751
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
7.738 × 10⁹³(94-digit number)
77385978933511659242…52225491524637277501
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.547 × 10⁹⁴(95-digit number)
15477195786702331848…04450983049274555001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
3.095 × 10⁹⁴(95-digit number)
30954391573404663696…08901966098549110001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
6.190 × 10⁹⁴(95-digit number)
61908783146809327393…17803932197098220001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.238 × 10⁹⁵(96-digit number)
12381756629361865478…35607864394196440001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.476 × 10⁹⁵(96-digit number)
24763513258723730957…71215728788392880001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
4.952 × 10⁹⁵(96-digit number)
49527026517447461915…42431457576785760001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
9.905 × 10⁹⁵(96-digit number)
99054053034894923830…84862915153571520001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.981 × 10⁹⁶(97-digit number)
19810810606978984766…69725830307143040001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
3.962 × 10⁹⁶(97-digit number)
39621621213957969532…39451660614286080001
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:57,913,926 XPM·at block #6,833,712 · 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