XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,648,707

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/4/2018, 5:01:34 PM Β· Difficulty 11.7665 Β· 4,192,372 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
626f1759bca81a3ddf1550b4a203f758bfec971ef6a73dec10f46795722f6674
View on Chainz β†—

Height

#2,648,707

Difficulty

11.766523

Transactions

1

Size

200 B

Version

2

Bits

0bc43adc

Nonce

955,527,831

Timestamp

5/4/2018, 5:01:34 PM

Confirmations

4,192,372

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

d2a69f5128e696a044b596a435af267a108c63a6f158de03bbcd06065cb1def9
Transactions (1)
Coinbased2a69f5128e696…cd06065cb1def9
1 in β†’ 1 out7.2100 XPM110 B
Adqah8zh…1WwoHJ9t
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.

1.258 Γ— 10⁹⁡(96-digit number)
12584272953817884996…30421888725436200959
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
1.258 Γ— 10⁹⁡(96-digit number)
12584272953817884996…30421888725436200959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.516 Γ— 10⁹⁡(96-digit number)
25168545907635769993…60843777450872401919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.033 Γ— 10⁹⁡(96-digit number)
50337091815271539986…21687554901744803839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.006 Γ— 10⁹⁢(97-digit number)
10067418363054307997…43375109803489607679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.013 Γ— 10⁹⁢(97-digit number)
20134836726108615994…86750219606979215359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.026 Γ— 10⁹⁢(97-digit number)
40269673452217231989…73500439213958430719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.053 Γ— 10⁹⁢(97-digit number)
80539346904434463978…47000878427916861439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.610 Γ— 10⁹⁷(98-digit number)
16107869380886892795…94001756855833722879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.221 Γ— 10⁹⁷(98-digit number)
32215738761773785591…88003513711667445759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.443 Γ— 10⁹⁷(98-digit number)
64431477523547571182…76007027423334891519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.288 Γ— 10⁹⁸(99-digit number)
12886295504709514236…52014054846669783039
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,972,995 XPMΒ·at block #6,841,078 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