XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,177,874

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/25/2017, 7:24:21 PM Β· Difficulty 10.9243 Β· 4,664,882 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7aae2872581d827c2fe0f4cf928715788070aa1cf42f4b2c5adddd334aace489
View on Chainz β†—

Height

#2,177,874

Difficulty

10.924330

Transactions

2

Size

426 B

Version

2

Bits

0aeca0e2

Nonce

157,591,004

Timestamp

6/25/2017, 7:24:21 PM

Confirmations

4,664,882

Mined by

⛏️ P2SHAHfNF358ZKYr7w1miiJ5gxMVqUVGMbag5D

Merkle Root

42f8d24fc45a5abc112ae1da70c0a035fb24b3c8ed899d03e0a8de0226b2ad76
Transactions (2)
Coinbase2b40b841d01479…394fee1c15e41e
1 in β†’ 1 out8.3800 XPM109 B
AHfNF358…VGMbag5D
9df0b1e4e049bb…e6c82a386842cd
1 in β†’ 2 out99989.1098 XPM227 B
AZYkJN7u…s8qMAwc7AXsA49Mn…gLwEcRuF
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.

4.773 Γ— 10⁹⁴(95-digit number)
47730514302279840631…67996347499568014679
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
4.773 Γ— 10⁹⁴(95-digit number)
47730514302279840631…67996347499568014679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
9.546 Γ— 10⁹⁴(95-digit number)
95461028604559681262…35992694999136029359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.909 Γ— 10⁹⁡(96-digit number)
19092205720911936252…71985389998272058719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.818 Γ— 10⁹⁡(96-digit number)
38184411441823872504…43970779996544117439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.636 Γ— 10⁹⁡(96-digit number)
76368822883647745009…87941559993088234879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.527 Γ— 10⁹⁢(97-digit number)
15273764576729549001…75883119986176469759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.054 Γ— 10⁹⁢(97-digit number)
30547529153459098003…51766239972352939519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.109 Γ— 10⁹⁢(97-digit number)
61095058306918196007…03532479944705879039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.221 Γ— 10⁹⁷(98-digit number)
12219011661383639201…07064959889411758079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.443 Γ— 10⁹⁷(98-digit number)
24438023322767278403…14129919778823516159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.887 Γ— 10⁹⁷(98-digit number)
48876046645534556806…28259839557647032319
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:57,986,385 XPMΒ·at block #6,842,755 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