XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,838,282

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/14/2018, 2:00:09 AM Β· Difficulty 11.7184 Β· 4,007,414 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a126b5696c1f4e98918ad55cb9a76393902072d7a1046d580d2b2079176440c9
View on Chainz β†—

Height

#2,838,282

Difficulty

11.718440

Transactions

1

Size

199 B

Version

2

Bits

0bb7ebae

Nonce

1,503,656,685

Timestamp

9/14/2018, 2:00:09 AM

Confirmations

4,007,414

Mined by

⛏️ P2SHALzaTxgXoAeYrVxzLbbYTrGRL3uwhF21HF

Merkle Root

61d7eab9f8e5c824d856a4cd9efdda7716906454ab581c8f84f45e4190d60c2e
Transactions (1)
Coinbase61d7eab9f8e5c8…f45e4190d60c2e
1 in β†’ 1 out7.2700 XPM110 B
ALzaTxgX…uwhF21HF
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.

5.954 Γ— 10⁹²(93-digit number)
59544596723913716398…63975724854086145339
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
5.954 Γ— 10⁹²(93-digit number)
59544596723913716398…63975724854086145339
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.190 Γ— 10⁹³(94-digit number)
11908919344782743279…27951449708172290679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.381 Γ— 10⁹³(94-digit number)
23817838689565486559…55902899416344581359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.763 Γ— 10⁹³(94-digit number)
47635677379130973118…11805798832689162719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.527 Γ— 10⁹³(94-digit number)
95271354758261946236…23611597665378325439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.905 Γ— 10⁹⁴(95-digit number)
19054270951652389247…47223195330756650879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.810 Γ— 10⁹⁴(95-digit number)
38108541903304778494…94446390661513301759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.621 Γ— 10⁹⁴(95-digit number)
76217083806609556989…88892781323026603519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.524 Γ— 10⁹⁡(96-digit number)
15243416761321911397…77785562646053207039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.048 Γ— 10⁹⁡(96-digit number)
30486833522643822795…55571125292106414079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
6.097 Γ— 10⁹⁡(96-digit number)
60973667045287645591…11142250584212828159
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:58,010,025 XPMΒ·at block #6,845,695 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