XPM Prime Explorer symbol
XPMPrime Explorer

Block #1,171,082

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/26/2015, 9:14:25 AM Β· Difficulty 10.9367 Β· 5,671,943 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3f0551038d8ac1a22ad44601433dd9aae2c4fa2b9c5e59c9456a8b8aabbe1375
View on Chainz β†—

Height

#1,171,082

Difficulty

10.936651

Transactions

1

Size

201 B

Version

2

Bits

0aefc85d

Nonce

158,576,165

Timestamp

7/26/2015, 9:14:25 AM

Confirmations

5,671,943

Mined by

⛏️ P2SHAK1xo33sDMfpJGSqZ5FFiKUwCQQwS3yNM9

Merkle Root

ca3bbd4a5c1a0e124849e17b7f626a9a681087f49335658291ac94252f982833
Transactions (1)
Coinbaseca3bbd4a5c1a0e…ac94252f982833
1 in β†’ 1 out8.3500 XPM110 B
AK1xo33s…QwS3yNM9
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.

4.265 Γ— 10⁹⁢(97-digit number)
42654286876286144607…72146895651563519999
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
4.265 Γ— 10⁹⁢(97-digit number)
42654286876286144607…72146895651563519999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.530 Γ— 10⁹⁢(97-digit number)
85308573752572289214…44293791303127039999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.706 Γ— 10⁹⁷(98-digit number)
17061714750514457842…88587582606254079999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.412 Γ— 10⁹⁷(98-digit number)
34123429501028915685…77175165212508159999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.824 Γ— 10⁹⁷(98-digit number)
68246859002057831371…54350330425016319999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.364 Γ— 10⁹⁸(99-digit number)
13649371800411566274…08700660850032639999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.729 Γ— 10⁹⁸(99-digit number)
27298743600823132548…17401321700065279999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.459 Γ— 10⁹⁸(99-digit number)
54597487201646265097…34802643400130559999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.091 Γ— 10⁹⁹(100-digit number)
10919497440329253019…69605286800261119999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.183 Γ— 10⁹⁹(100-digit number)
21838994880658506038…39210573600522239999
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:57,988,554 XPMΒ·at block #6,843,024 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