XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,162,515

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/16/2017, 1:41:06 AM Β· Difficulty 10.9009 Β· 4,663,670 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5367905ea90f44eb4720b2dd34827ed047faa52435dfa5d1468805f50f4c21a0
View on Chainz β†—

Height

#2,162,515

Difficulty

10.900891

Transactions

2

Size

3.16 KB

Version

2

Bits

0ae6a0cd

Nonce

89,847,622

Timestamp

6/16/2017, 1:41:06 AM

Confirmations

4,663,670

Mined by

⛏️ P2SHAKxLygJXdro8ESp2A8vrDuCegr3L4CHj2i

Merkle Root

5ae42ecf09c1d7fe15d76b451203e5bc732889d962ecb89434cdea7aefba3354
Transactions (2)
Coinbase091266d12b120c…4634c76a3f17ba
1 in β†’ 1 out8.4600 XPM110 B
AKxLygJX…3L4CHj2i
65c93812f01c2c…b84d2809306460
20 in β†’ 2 out2302.4241 XPM2.96 KB
Adzr3PHS…5EwVUFTFAc6a15ef…dt17kLNP
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.

2.216 Γ— 10⁹⁴(95-digit number)
22165571749465754356…87629924504358420481
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
2.216 Γ— 10⁹⁴(95-digit number)
22165571749465754356…87629924504358420481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.433 Γ— 10⁹⁴(95-digit number)
44331143498931508712…75259849008716840961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.866 Γ— 10⁹⁴(95-digit number)
88662286997863017425…50519698017433681921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.773 Γ— 10⁹⁡(96-digit number)
17732457399572603485…01039396034867363841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.546 Γ— 10⁹⁡(96-digit number)
35464914799145206970…02078792069734727681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.092 Γ— 10⁹⁡(96-digit number)
70929829598290413940…04157584139469455361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.418 Γ— 10⁹⁢(97-digit number)
14185965919658082788…08315168278938910721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.837 Γ— 10⁹⁢(97-digit number)
28371931839316165576…16630336557877821441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.674 Γ— 10⁹⁢(97-digit number)
56743863678632331152…33260673115755642881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.134 Γ— 10⁹⁷(98-digit number)
11348772735726466230…66521346231511285761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.269 Γ— 10⁹⁷(98-digit number)
22697545471452932460…33042692463022571521
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:57,853,609 XPMΒ·at block #6,826,184 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