XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,634,389

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/28/2018, 9:10:30 PM Β· Difficulty 11.2422 Β· 4,196,605 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b2cae68577e0f85a2b9da11777b29d544cd8583108bf203035bd181fdcb723a4
View on Chainz β†—

Height

#2,634,389

Difficulty

11.242165

Transactions

2

Size

426 B

Version

2

Bits

0b3dfe83

Nonce

1,151,787,378

Timestamp

4/28/2018, 9:10:30 PM

Confirmations

4,196,605

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

74bb714b0aba2fd169a250d781abfe0e7aa9698cb8fcca75e975556102e096a4
Transactions (2)
Coinbase2c9964416de5f1…56a7d392cf2693
1 in β†’ 1 out7.9100 XPM110 B
Adqah8zh…1WwoHJ9t
3069d999ca9cd3…b1cffc0ffea0fc
1 in β†’ 2 out18.2666 XPM226 B
AGWuB6uH…qZVt9vF6ALFCjDjB…XEfXtzaq
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.

5.014 Γ— 10⁹⁴(95-digit number)
50142038735222175742…46937437546006352001
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
5.014 Γ— 10⁹⁴(95-digit number)
50142038735222175742…46937437546006352001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.002 Γ— 10⁹⁡(96-digit number)
10028407747044435148…93874875092012704001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.005 Γ— 10⁹⁡(96-digit number)
20056815494088870296…87749750184025408001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.011 Γ— 10⁹⁡(96-digit number)
40113630988177740593…75499500368050816001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.022 Γ— 10⁹⁡(96-digit number)
80227261976355481187…50999000736101632001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.604 Γ— 10⁹⁢(97-digit number)
16045452395271096237…01998001472203264001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.209 Γ— 10⁹⁢(97-digit number)
32090904790542192474…03996002944406528001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.418 Γ— 10⁹⁢(97-digit number)
64181809581084384949…07992005888813056001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.283 Γ— 10⁹⁷(98-digit number)
12836361916216876989…15984011777626112001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.567 Γ— 10⁹⁷(98-digit number)
25672723832433753979…31968023555252224001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
5.134 Γ— 10⁹⁷(98-digit number)
51345447664867507959…63936047110504448001
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:57,892,093 XPMΒ·at block #6,830,993 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