XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,174,559

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/23/2017, 11:46:10 PM Β· Difficulty 10.9130 Β· 4,665,016 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8447a04dfaa91c034b4cab88451df1e5fe1885bf52e0ad780c1bf9e2f1fca154
View on Chainz β†—

Height

#2,174,559

Difficulty

10.913009

Transactions

1

Size

199 B

Version

2

Bits

0ae9baf9

Nonce

72,150,453

Timestamp

6/23/2017, 11:46:10 PM

Confirmations

4,665,016

Mined by

⛏️ P2SHALJbqFqmKFfuugng5gYR22TuX7XTnmhQhQ

Merkle Root

e5ccef0bd458f23897494f45b0c919f9ce97cf3c0aff12b3d3c1e40876b7a283
Transactions (1)
Coinbasee5ccef0bd458f2…c1e40876b7a283
1 in β†’ 1 out8.3800 XPM109 B
ALJbqFqm…XTnmhQhQ
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.

1.961 Γ— 10⁹⁴(95-digit number)
19613712375586998783…19530554023551661699
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
1.961 Γ— 10⁹⁴(95-digit number)
19613712375586998783…19530554023551661699
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.922 Γ— 10⁹⁴(95-digit number)
39227424751173997566…39061108047103323399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.845 Γ— 10⁹⁴(95-digit number)
78454849502347995132…78122216094206646799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.569 Γ— 10⁹⁡(96-digit number)
15690969900469599026…56244432188413293599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.138 Γ— 10⁹⁡(96-digit number)
31381939800939198053…12488864376826587199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.276 Γ— 10⁹⁡(96-digit number)
62763879601878396106…24977728753653174399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.255 Γ— 10⁹⁢(97-digit number)
12552775920375679221…49955457507306348799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.510 Γ— 10⁹⁢(97-digit number)
25105551840751358442…99910915014612697599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.021 Γ— 10⁹⁢(97-digit number)
50211103681502716884…99821830029225395199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.004 Γ— 10⁹⁷(98-digit number)
10042220736300543376…99643660058450790399
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:57,960,886 XPMΒ·at block #6,839,574 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