XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,096,320

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/1/2017, 10:23:15 PM Β· Difficulty 10.8717 Β· 4,746,779 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f1c088fd3f5f74799f65429e5535be9f173b5576ce7d7e69797170cd4b7df417
View on Chainz β†—

Height

#2,096,320

Difficulty

10.871693

Transactions

1

Size

199 B

Version

2

Bits

0adf274b

Nonce

1,346,358,192

Timestamp

5/1/2017, 10:23:15 PM

Confirmations

4,746,779

Mined by

⛏️ P2SHAJAByP7NyeWnDsyvhxe5o22EkvQmE2BTzZ

Merkle Root

852a64fcac3bf4a8f504b27202b2958c97551ae44dade471395192d0f165393b
Transactions (1)
Coinbase852a64fcac3bf4…5192d0f165393b
1 in β†’ 1 out8.4500 XPM109 B
AJAByP7N…QmE2BTzZ
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.

1.566 Γ— 10⁹⁴(95-digit number)
15664314000969772706…15259640708576229221
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
1.566 Γ— 10⁹⁴(95-digit number)
15664314000969772706…15259640708576229221
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.132 Γ— 10⁹⁴(95-digit number)
31328628001939545412…30519281417152458441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.265 Γ— 10⁹⁴(95-digit number)
62657256003879090825…61038562834304916881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.253 Γ— 10⁹⁡(96-digit number)
12531451200775818165…22077125668609833761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.506 Γ— 10⁹⁡(96-digit number)
25062902401551636330…44154251337219667521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.012 Γ— 10⁹⁡(96-digit number)
50125804803103272660…88308502674439335041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.002 Γ— 10⁹⁢(97-digit number)
10025160960620654532…76617005348878670081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.005 Γ— 10⁹⁢(97-digit number)
20050321921241309064…53234010697757340161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.010 Γ— 10⁹⁢(97-digit number)
40100643842482618128…06468021395514680321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
8.020 Γ— 10⁹⁢(97-digit number)
80201287684965236256…12936042791029360641
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:57,989,155 XPMΒ·at block #6,843,098 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