XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,160,507

1CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the First Kind Β· Discovered 6/14/2017, 3:40:58 PM Β· Difficulty 10.9015 Β· 4,669,942 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a596c862646caea055d089128a15e6eec4a2dff62498f8db8fb6409637bcc06f
View on Chainz β†—

Height

#2,160,507

Difficulty

10.901460

Transactions

2

Size

2.00 KB

Version

2

Bits

0ae6c61b

Nonce

309,691,364

Timestamp

6/14/2017, 3:40:58 PM

Confirmations

4,669,942

Mined by

⛏️ P2SHAHR5G12owbZ4kWCYzSB6FD6PwJu9jMRaEV

Merkle Root

4bdaab45cdcd243be68b606fa4ca71128459c55be45dfd43c1ffb27c1e30e905
Transactions (2)
Coinbase13e0dfa60ea135…c1b0fee2faa063
1 in β†’ 1 out8.4400 XPM110 B
AHR5G12o…u9jMRaEV
5c121653e8ea06…55856abe5e9a0f
12 in β†’ 2 out2134.8449 XPM1.81 KB
ANrz4YsW…8yK8tTuZAZ7xo3ni…aXTAFhZR
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.

5.617 Γ— 10⁹³(94-digit number)
56179415493272221805…97729316663368151599
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
5.617 Γ— 10⁹³(94-digit number)
56179415493272221805…97729316663368151599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.123 Γ— 10⁹⁴(95-digit number)
11235883098654444361…95458633326736303199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.247 Γ— 10⁹⁴(95-digit number)
22471766197308888722…90917266653472606399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.494 Γ— 10⁹⁴(95-digit number)
44943532394617777444…81834533306945212799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.988 Γ— 10⁹⁴(95-digit number)
89887064789235554888…63669066613890425599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.797 Γ— 10⁹⁡(96-digit number)
17977412957847110977…27338133227780851199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.595 Γ— 10⁹⁡(96-digit number)
35954825915694221955…54676266455561702399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.190 Γ— 10⁹⁡(96-digit number)
71909651831388443910…09352532911123404799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.438 Γ— 10⁹⁢(97-digit number)
14381930366277688782…18705065822246809599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.876 Γ— 10⁹⁢(97-digit number)
28763860732555377564…37410131644493619199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
5.752 Γ— 10⁹⁢(97-digit number)
57527721465110755128…74820263288987238399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
12
2^11 Γ— origin βˆ’ 1
1.150 Γ— 10⁹⁷(98-digit number)
11505544293022151025…49640526577974476799
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 consecutive prime numbers forming a Cunningham Chain of the First 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
ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,887,836 XPMΒ·at block #6,830,448 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