XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,160,258

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/14/2017, 11:01:46 AM Β· Difficulty 10.9021 Β· 4,654,035 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7e91f119965ec2e358bdaff56402036144d96913bdccf16052cb2f2fc4d4c0da
View on Chainz β†—

Height

#2,160,258

Difficulty

10.902051

Transactions

2

Size

3.99 KB

Version

2

Bits

0ae6eccb

Nonce

2,099,169,156

Timestamp

6/14/2017, 11:01:46 AM

Confirmations

4,654,035

Mined by

⛏️ P2SHAKG9MSU1T9BJzioUvUp6wELtaHnjG4QYSp

Merkle Root

a549ac5f33bc78de86d6ac0f0a03861c90ac97eda0f04d7962049815513fc105
Transactions (2)
Coinbase934128a4d3c5e4…7ea395c9617674
1 in β†’ 1 out8.4500 XPM109 B
AKG9MSU1…njG4QYSp
43f1f354d53508…52e3f3bbd36467
26 in β†’ 1 out1400.0000 XPM3.80 KB
AbgPUjdU…nN9We5Xi
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.

1.090 Γ— 10⁹⁢(97-digit number)
10906720315976838195…04839440303395552001
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
1.090 Γ— 10⁹⁢(97-digit number)
10906720315976838195…04839440303395552001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.181 Γ— 10⁹⁢(97-digit number)
21813440631953676390…09678880606791104001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.362 Γ— 10⁹⁢(97-digit number)
43626881263907352780…19357761213582208001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.725 Γ— 10⁹⁢(97-digit number)
87253762527814705561…38715522427164416001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.745 Γ— 10⁹⁷(98-digit number)
17450752505562941112…77431044854328832001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.490 Γ— 10⁹⁷(98-digit number)
34901505011125882224…54862089708657664001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.980 Γ— 10⁹⁷(98-digit number)
69803010022251764449…09724179417315328001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.396 Γ— 10⁹⁸(99-digit number)
13960602004450352889…19448358834630656001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.792 Γ— 10⁹⁸(99-digit number)
27921204008900705779…38896717669261312001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.584 Γ— 10⁹⁸(99-digit number)
55842408017801411559…77793435338522624001
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:57,758,407 XPMΒ·at block #6,814,292 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