XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,132,278

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/25/2017, 4:36:50 PM Β· Difficulty 10.9103 Β· 4,709,499 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
49d07e4dbe66643ff2b256c5ee4956f245bbf29c2afc5dc012959e86a428f0dc
View on Chainz β†—

Height

#2,132,278

Difficulty

10.910275

Transactions

1

Size

199 B

Version

2

Bits

0ae907cc

Nonce

499,672,866

Timestamp

5/25/2017, 4:36:50 PM

Confirmations

4,709,499

Mined by

⛏️ P2SHAXy1gw6Qa5cN9URNGnfkYk9QUdT53WzKZE

Merkle Root

b0bc8adc0c2e5c3c6709590183b412c86a4f269e8ef50135eb84c31fb647742c
Transactions (1)
Coinbaseb0bc8adc0c2e5c…84c31fb647742c
1 in β†’ 1 out8.3900 XPM109 B
AXy1gw6Q…T53WzKZE
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.716 Γ— 10⁹⁡(96-digit number)
17166713154310852058…92520142200259598401
Discovered Prime Numbers
p_k = 2^k Γ— 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
1.716 Γ— 10⁹⁡(96-digit number)
17166713154310852058…92520142200259598401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.433 Γ— 10⁹⁡(96-digit number)
34333426308621704116…85040284400519196801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.866 Γ— 10⁹⁡(96-digit number)
68666852617243408233…70080568801038393601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.373 Γ— 10⁹⁢(97-digit number)
13733370523448681646…40161137602076787201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.746 Γ— 10⁹⁢(97-digit number)
27466741046897363293…80322275204153574401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.493 Γ— 10⁹⁢(97-digit number)
54933482093794726586…60644550408307148801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.098 Γ— 10⁹⁷(98-digit number)
10986696418758945317…21289100816614297601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.197 Γ— 10⁹⁷(98-digit number)
21973392837517890634…42578201633228595201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.394 Γ— 10⁹⁷(98-digit number)
43946785675035781269…85156403266457190401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
8.789 Γ— 10⁹⁷(98-digit number)
87893571350071562538…70312806532914380801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.757 Γ— 10⁹⁸(99-digit number)
17578714270014312507…40625613065828761601
Verify on FactorDB β†—Wolfram Alpha β†—

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 β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜…β˜†β˜†
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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,978,592 XPMΒ·at block #6,841,776 Β· 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 PolicyΒ·
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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.

Β·Privacy Policy