XPM Prime Explorer symbol
XPMPrime Explorer

Block #107,565

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/9/2013, 2:20:20 PM Β· Difficulty 9.6306 Β· 6,707,481 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1d36d8227602226251d1147e24cc3197d69f22bb6f69056a41897c4fc4a6dc7a
View on Chainz β†—

Height

#107,565

Difficulty

9.630648

Transactions

2

Size

689 B

Version

2

Bits

09a17222

Nonce

390,244

Timestamp

8/9/2013, 2:20:20 PM

Confirmations

6,707,481

Mined by

⛏️ P2SHALDLgVCFuZznMcL61X5722rfJf4YUqxRBS

Merkle Root

ce971b6c7cbae2e384d9bfaef52cfcd541a539cc5b195dfe52c59ae93b8e671b
Transactions (2)
Coinbasef3f7e941bdf2e3…066907f6892eb1
1 in β†’ 1 out10.7800 XPM109 B
ALDLgVCF…4YUqxRBS
d5d8f55e4ad595…2997294a6a6afb
3 in β†’ 1 out3000.0000 XPM491 B
AerT7Pbd…3qYqmAEe
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.

1.145 Γ— 10⁹³(94-digit number)
11459689290435108379…62268229105235130899
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
1.145 Γ— 10⁹³(94-digit number)
11459689290435108379…62268229105235130899
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.291 Γ— 10⁹³(94-digit number)
22919378580870216758…24536458210470261799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.583 Γ— 10⁹³(94-digit number)
45838757161740433517…49072916420940523599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.167 Γ— 10⁹³(94-digit number)
91677514323480867035…98145832841881047199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.833 Γ— 10⁹⁴(95-digit number)
18335502864696173407…96291665683762094399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.667 Γ— 10⁹⁴(95-digit number)
36671005729392346814…92583331367524188799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.334 Γ— 10⁹⁴(95-digit number)
73342011458784693628…85166662735048377599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.466 Γ— 10⁹⁡(96-digit number)
14668402291756938725…70333325470096755199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.933 Γ— 10⁹⁡(96-digit number)
29336804583513877451…40666650940193510399
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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 9

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:57,764,458 XPMΒ·at block #6,815,045 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