XPM Prime Explorer symbol
XPMPrime Explorer

Block #1,873,035

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/1/2016, 12:40:06 AM Β· Difficulty 10.6700 Β· 4,960,504 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
df3ebe3809b65a9a8818d5edb96b74023cb5d23777f331101d5bbb7b01f641cc
View on Chainz β†—

Height

#1,873,035

Difficulty

10.670038

Transactions

2

Size

722 B

Version

2

Bits

0aab879f

Nonce

358,472,301

Timestamp

12/1/2016, 12:40:06 AM

Confirmations

4,960,504

Mined by

⛏️ P2SHAPYexirhv72JVWJHXsTHzdSCB99CPvivnv

Merkle Root

654fb953e064a3abb4d3028e626cbe31b01e424e113020be76732adfb43223f0
Transactions (2)
Coinbase590f8dbb3e8959…4f84d5375527c2
1 in β†’ 1 out8.7800 XPM110 B
APYexirh…9CPvivnv
1bdec2878ad979…aabbe8e61cbe36
3 in β†’ 2 out73.0907 XPM522 B
ARazQio2…C6g89wmVASMMZz4E…7FeHYYcp
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.

8.269 Γ— 10⁹⁡(96-digit number)
82695645045000066842…87436160168250457599
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
8.269 Γ— 10⁹⁡(96-digit number)
82695645045000066842…87436160168250457599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.653 Γ— 10⁹⁢(97-digit number)
16539129009000013368…74872320336500915199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.307 Γ— 10⁹⁢(97-digit number)
33078258018000026736…49744640673001830399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.615 Γ— 10⁹⁢(97-digit number)
66156516036000053473…99489281346003660799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.323 Γ— 10⁹⁷(98-digit number)
13231303207200010694…98978562692007321599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.646 Γ— 10⁹⁷(98-digit number)
26462606414400021389…97957125384014643199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.292 Γ— 10⁹⁷(98-digit number)
52925212828800042779…95914250768029286399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.058 Γ— 10⁹⁸(99-digit number)
10585042565760008555…91828501536058572799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.117 Γ— 10⁹⁸(99-digit number)
21170085131520017111…83657003072117145599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.234 Γ— 10⁹⁸(99-digit number)
42340170263040034223…67314006144234291199
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 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
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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,912,511 XPMΒ·at block #6,833,538 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