XPM Prime Explorer symbol
XPMPrime Explorer

Block #847,103

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/10/2014, 3:04:08 AM Β· Difficulty 10.9719 Β· 5,995,171 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
be2236a4f57ff5918d150e47f0f5b6c32b73b8cee49a580a2fb4d0bc6046b018
View on Chainz β†—

Height

#847,103

Difficulty

10.971881

Transactions

2

Size

426 B

Version

2

Bits

0af8cd2b

Nonce

200,877,469

Timestamp

12/10/2014, 3:04:08 AM

Confirmations

5,995,171

Mined by

⛏️ P2SHANHEToFWoV499DM3dRaoqqxt8WupT6i5zt

Merkle Root

25b694795ffcb4fee077db4e841a60ff68445e633311a6bc0402f7934c0e9631
Transactions (2)
Coinbase27fe67f5b64fc0…55bf3748fc5492
1 in β†’ 1 out8.3050 XPM110 B
ANHEToFW…upT6i5zt
2e7cecd3dcb582…b036fc3c7460f9
1 in β†’ 2 out0.0549 XPM226 B
Ab7ky5a9…P7Ju4tLpAS7pXP1E…gsyMUmbx
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.

1.154 Γ— 10⁹⁡(96-digit number)
11548660348525411542…10817421223138867199
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
1.154 Γ— 10⁹⁡(96-digit number)
11548660348525411542…10817421223138867199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.309 Γ— 10⁹⁡(96-digit number)
23097320697050823085…21634842446277734399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.619 Γ— 10⁹⁡(96-digit number)
46194641394101646171…43269684892555468799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.238 Γ— 10⁹⁡(96-digit number)
92389282788203292343…86539369785110937599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.847 Γ— 10⁹⁢(97-digit number)
18477856557640658468…73078739570221875199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.695 Γ— 10⁹⁢(97-digit number)
36955713115281316937…46157479140443750399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.391 Γ— 10⁹⁢(97-digit number)
73911426230562633875…92314958280887500799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.478 Γ— 10⁹⁷(98-digit number)
14782285246112526775…84629916561775001599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.956 Γ— 10⁹⁷(98-digit number)
29564570492225053550…69259833123550003199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.912 Γ— 10⁹⁷(98-digit number)
59129140984450107100…38519666247100006399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.182 Γ— 10⁹⁸(99-digit number)
11825828196890021420…77039332494200012799
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:57,982,593 XPMΒ·at block #6,842,273 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