Block #2,617,450

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 4/17/2018, 3:51:50 AM · Difficulty 11.2324 · 4,225,864 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
97370901c311b61ecb89a5608f052d525af75a5c4628442dbbfadff0d42fd78b

Height

#2,617,450

Difficulty

11.232405

Transactions

5

Size

1.34 KB

Version

2

Bits

0b3b7ee2

Nonce

1,209,346,997

Timestamp

4/17/2018, 3:51:50 AM

Confirmations

4,225,864

Merkle Root

93440b4d668f9d55bbe5219dba8148b06192040f73f17fe1818739a1ce6aff75
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.

6.321 × 10⁹⁶(97-digit number)
63218860122409697475…26612545885036154881
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
6.321 × 10⁹⁶(97-digit number)
63218860122409697475…26612545885036154881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.264 × 10⁹⁷(98-digit number)
12643772024481939495…53225091770072309761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.528 × 10⁹⁷(98-digit number)
25287544048963878990…06450183540144619521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
5.057 × 10⁹⁷(98-digit number)
50575088097927757980…12900367080289239041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.011 × 10⁹⁸(99-digit number)
10115017619585551596…25800734160578478081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.023 × 10⁹⁸(99-digit number)
20230035239171103192…51601468321156956161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
4.046 × 10⁹⁸(99-digit number)
40460070478342206384…03202936642313912321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
8.092 × 10⁹⁸(99-digit number)
80920140956684412768…06405873284627824641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.618 × 10⁹⁹(100-digit number)
16184028191336882553…12811746569255649281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.236 × 10⁹⁹(100-digit number)
32368056382673765107…25623493138511298561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
6.473 × 10⁹⁹(100-digit number)
64736112765347530214…51246986277022597121
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:57,990,870 XPM·at block #6,843,313 · 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