Block #2,614,927

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 4/15/2018, 11:28:42 AM · Difficulty 11.2169 · 4,225,992 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a539a66a7cef7761b5320c746785b668580be10645c446965399887fa9b1b980

Height

#2,614,927

Difficulty

11.216899

Transactions

2

Size

8.04 KB

Version

2

Bits

0b3786b6

Nonce

393,986,592

Timestamp

4/15/2018, 11:28:42 AM

Confirmations

4,225,992

Merkle Root

8023c518e479c8c683bb620caa9ec4a3dedb09a83e6546dc683cbb6414e02857
Transactions (2)
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.

2.889 × 10⁹⁵(96-digit number)
28894840847576220082…56452770795156246401
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
2.889 × 10⁹⁵(96-digit number)
28894840847576220082…56452770795156246401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
5.778 × 10⁹⁵(96-digit number)
57789681695152440164…12905541590312492801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.155 × 10⁹⁶(97-digit number)
11557936339030488032…25811083180624985601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.311 × 10⁹⁶(97-digit number)
23115872678060976065…51622166361249971201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
4.623 × 10⁹⁶(97-digit number)
46231745356121952131…03244332722499942401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
9.246 × 10⁹⁶(97-digit number)
92463490712243904262…06488665444999884801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.849 × 10⁹⁷(98-digit number)
18492698142448780852…12977330889999769601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.698 × 10⁹⁷(98-digit number)
36985396284897561705…25954661779999539201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
7.397 × 10⁹⁷(98-digit number)
73970792569795123410…51909323559999078401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.479 × 10⁹⁸(99-digit number)
14794158513959024682…03818647119998156801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
2.958 × 10⁹⁸(99-digit number)
29588317027918049364…07637294239996313601
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:57,971,703 XPM·at block #6,840,918 · 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