XPM Prime Explorer symbol
XPMPrime Explorer

Block #175,832

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/22/2013, 1:33:28 PM Β· Difficulty 9.8643 Β· 6,634,123 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
bfa576a248e40b12f93b0415dabf3e9f4fb11e4058b63a23eedf41e76f3251f2
View on Chainz β†—

Height

#175,832

Difficulty

9.864315

Transactions

2

Size

425 B

Version

2

Bits

09dd43b9

Nonce

196,574

Timestamp

9/22/2013, 1:33:28 PM

Confirmations

6,634,123

Mined by

⛏️ P2SHAWWFn2wtF1uA7N4c51XsLnZBxW447GdZy3

Merkle Root

aaf409d115a307a20e657337206a95e512306002f963a23567a086dacad92075
Transactions (2)
Coinbasec89d331953f8bb…2f6cd4d24cb92a
1 in β†’ 1 out10.2700 XPM109 B
AWWFn2wt…447GdZy3
c811ef8932c3b3…ee991170a0466c
1 in β†’ 2 out2.7629 XPM227 B
AcN7Mwej…Rnr1man2AZs4bVcL…KUwpaC6e
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.

3.180 Γ— 10⁹³(94-digit number)
31804269393028374107…31143726595932987791
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
3.180 Γ— 10⁹³(94-digit number)
31804269393028374107…31143726595932987791
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.360 Γ— 10⁹³(94-digit number)
63608538786056748214…62287453191865975581
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.272 Γ— 10⁹⁴(95-digit number)
12721707757211349642…24574906383731951161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.544 Γ— 10⁹⁴(95-digit number)
25443415514422699285…49149812767463902321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.088 Γ— 10⁹⁴(95-digit number)
50886831028845398571…98299625534927804641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.017 Γ— 10⁹⁡(96-digit number)
10177366205769079714…96599251069855609281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.035 Γ— 10⁹⁡(96-digit number)
20354732411538159428…93198502139711218561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.070 Γ— 10⁹⁡(96-digit number)
40709464823076318857…86397004279422437121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.141 Γ— 10⁹⁡(96-digit number)
81418929646152637714…72794008558844874241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.628 Γ— 10⁹⁢(97-digit number)
16283785929230527542…45588017117689748481
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,723,721 XPMΒ·at block #6,809,954 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.
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