XPM Prime Explorer symbol
XPMPrime Explorer

Block #16,814

1CCLength 7β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/11/2013, 11:44:05 PM Β· Difficulty 7.8816 Β· 6,810,015 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c8139e00f234cda984efdf84e7742c310aced33b00e88dc1151edcd80564f449
View on Chainz β†—

Height

#16,814

Difficulty

7.881556

Transactions

1

Size

200 B

Version

2

Bits

07e1adae

Nonce

402

Timestamp

7/11/2013, 11:44:05 PM

Confirmations

6,810,015

Mined by

⛏️ P2SHATdcg5aGsKSGVEp9Y9eFvZwDgeu44DE6Kp

Merkle Root

0432c9b2645b181111aea7be862092fc3c5c2fca8901e507c27cf844d6e2fdd6
Transactions (1)
Coinbase0432c9b2645b18…7cf844d6e2fdd6
1 in β†’ 1 out16.0800 XPM109 B
ATdcg5aG…u44DE6Kp
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.

4.281 Γ— 10⁹⁢(97-digit number)
42810866730894557186…11120133308082463359
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
4.281 Γ— 10⁹⁢(97-digit number)
42810866730894557186…11120133308082463359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.562 Γ— 10⁹⁢(97-digit number)
85621733461789114373…22240266616164926719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.712 Γ— 10⁹⁷(98-digit number)
17124346692357822874…44480533232329853439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.424 Γ— 10⁹⁷(98-digit number)
34248693384715645749…88961066464659706879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.849 Γ— 10⁹⁷(98-digit number)
68497386769431291499…77922132929319413759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.369 Γ— 10⁹⁸(99-digit number)
13699477353886258299…55844265858638827519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.739 Γ— 10⁹⁸(99-digit number)
27398954707772516599…11688531717277655039
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 7 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
CommonChain length 7

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,858,798 XPMΒ·at block #6,826,828 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