XPM Prime Explorer symbol
XPMPrime Explorer

Block #3,324,658

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/24/2019, 6:32:33 AM Β· Difficulty 11.0219 Β· 3,515,913 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a1d12369c621325b248b2926f5d108df07376ad306059ca14d64ad12313b80e6
View on Chainz β†—

Height

#3,324,658

Difficulty

11.021949

Transactions

2

Size

393 B

Version

2

Bits

0b059e6b

Nonce

1,405,007,416

Timestamp

8/24/2019, 6:32:33 AM

Confirmations

3,515,913

Mined by

⛏️ P2SHAa32y8PQmrraS9AMzCsmSNxawTe3Enbehj

Merkle Root

94bacf9c15fc5040f5df6ccab5d88a0903947e66674efadcb401dfcba2bb55e0
Transactions (2)
Coinbase12305cdfba857d…388fee00f6e05c
1 in β†’ 1 out8.2300 XPM110 B
Aa32y8PQ…e3Enbehj
4dfbd2da90a358…37f4009aa6ec54
1 in β†’ 1 out3.9900 XPM193 B
AeTHTL7A…vT1872bk
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.

3.538 Γ— 10⁹⁴(95-digit number)
35386893585047978898…29288153096985464321
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
3.538 Γ— 10⁹⁴(95-digit number)
35386893585047978898…29288153096985464321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.077 Γ— 10⁹⁴(95-digit number)
70773787170095957797…58576306193970928641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.415 Γ— 10⁹⁡(96-digit number)
14154757434019191559…17152612387941857281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.830 Γ— 10⁹⁡(96-digit number)
28309514868038383118…34305224775883714561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.661 Γ— 10⁹⁡(96-digit number)
56619029736076766237…68610449551767429121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.132 Γ— 10⁹⁢(97-digit number)
11323805947215353247…37220899103534858241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.264 Γ— 10⁹⁢(97-digit number)
22647611894430706495…74441798207069716481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.529 Γ— 10⁹⁢(97-digit number)
45295223788861412990…48883596414139432961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.059 Γ— 10⁹⁢(97-digit number)
90590447577722825980…97767192828278865921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.811 Γ— 10⁹⁷(98-digit number)
18118089515544565196…95534385656557731841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.623 Γ— 10⁹⁷(98-digit number)
36236179031089130392…91068771313115463681
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:57,968,903 XPMΒ·at block #6,840,570 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