XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,644,788

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/2/2018, 3:37:36 PM Β· Difficulty 11.7176 Β· 4,186,823 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5e4ab27cd0c5ee7c7ef674af7354339b9beae31c34efae22232c28f47166e89a
View on Chainz β†—

Height

#2,644,788

Difficulty

11.717632

Transactions

1

Size

201 B

Version

2

Bits

0bb7b6bc

Nonce

1,072,139,370

Timestamp

5/2/2018, 3:37:36 PM

Confirmations

4,186,823

Mined by

⛏️ P2SHAStHEkq7aaQf2cRKQMoCpRMMsniJ3WScnt

Merkle Root

e46efd0df4ab8aa63ede6c2da0e2bd5f0e09a13eb87f6409ced31ac437d6ec26
Transactions (1)
Coinbasee46efd0df4ab8a…d31ac437d6ec26
1 in β†’ 1 out7.2700 XPM110 B
AStHEkq7…iJ3WScnt
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.

6.107 Γ— 10⁹⁢(97-digit number)
61077596777959067036…90840916200670902401
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
6.107 Γ— 10⁹⁢(97-digit number)
61077596777959067036…90840916200670902401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.221 Γ— 10⁹⁷(98-digit number)
12215519355591813407…81681832401341804801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.443 Γ— 10⁹⁷(98-digit number)
24431038711183626814…63363664802683609601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.886 Γ— 10⁹⁷(98-digit number)
48862077422367253629…26727329605367219201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.772 Γ— 10⁹⁷(98-digit number)
97724154844734507259…53454659210734438401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.954 Γ— 10⁹⁸(99-digit number)
19544830968946901451…06909318421468876801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.908 Γ— 10⁹⁸(99-digit number)
39089661937893802903…13818636842937753601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.817 Γ— 10⁹⁸(99-digit number)
78179323875787605807…27637273685875507201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.563 Γ— 10⁹⁹(100-digit number)
15635864775157521161…55274547371751014401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.127 Γ— 10⁹⁹(100-digit number)
31271729550315042322…10549094743502028801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
6.254 Γ— 10⁹⁹(100-digit number)
62543459100630084645…21098189487004057601
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:57,896,988 XPMΒ·at block #6,831,610 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