Block #2,487,017

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/23/2018, 9:58:05 PM · Difficulty 10.9689 · 4,354,812 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d5e01979b0ecef13e94ebc301fa98cae2b230c42f6cdd6f6b307448a909ebd27

Height

#2,487,017

Difficulty

10.968889

Transactions

38

Size

7.75 KB

Version

2

Bits

0af80924

Nonce

1,766,202,296

Timestamp

1/23/2018, 9:58:05 PM

Confirmations

4,354,812

Merkle Root

cf045f5ad63e89b2abb00e6b2d6e3ad687abb9b4093bfa2fa677322578a253c1
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.

1.066 × 10⁹⁶(97-digit number)
10666419276102322547…07875879754750410241
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
1.066 × 10⁹⁶(97-digit number)
10666419276102322547…07875879754750410241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.133 × 10⁹⁶(97-digit number)
21332838552204645095…15751759509500820481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
4.266 × 10⁹⁶(97-digit number)
42665677104409290190…31503519019001640961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
8.533 × 10⁹⁶(97-digit number)
85331354208818580381…63007038038003281921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.706 × 10⁹⁷(98-digit number)
17066270841763716076…26014076076006563841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.413 × 10⁹⁷(98-digit number)
34132541683527432152…52028152152013127681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
6.826 × 10⁹⁷(98-digit number)
68265083367054864305…04056304304026255361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.365 × 10⁹⁸(99-digit number)
13653016673410972861…08112608608052510721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.730 × 10⁹⁸(99-digit number)
27306033346821945722…16225217216105021441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
5.461 × 10⁹⁸(99-digit number)
54612066693643891444…32450434432210042881
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,979,005 XPM·at block #6,841,828 · 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