XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,685,654

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/31/2018, 9:23:56 AM Β· Difficulty 11.6884 Β· 4,157,270 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
55871b845f795c38e751d930c2729c5e7e4f9091cd4e7d8cb589df99c8e298e0
View on Chainz β†—

Height

#2,685,654

Difficulty

11.688381

Transactions

1

Size

200 B

Version

2

Bits

0bb039b8

Nonce

779,360,250

Timestamp

5/31/2018, 9:23:56 AM

Confirmations

4,157,270

Mined by

⛏️ P2SHAKjTNi39JfUHXD4uowBJe5FssqHmG7v4Ng

Merkle Root

bf1d74d83aa1956e3685f175f93e169c002e3c9f51f1b638a8dd3a63d479563f
Transactions (1)
Coinbasebf1d74d83aa195…dd3a63d479563f
1 in β†’ 1 out7.3100 XPM110 B
AKjTNi39…HmG7v4Ng
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.

1.155 Γ— 10⁹⁡(96-digit number)
11552096972057932793…33303827683628557279
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
1.155 Γ— 10⁹⁡(96-digit number)
11552096972057932793…33303827683628557279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.310 Γ— 10⁹⁡(96-digit number)
23104193944115865587…66607655367257114559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.620 Γ— 10⁹⁡(96-digit number)
46208387888231731175…33215310734514229119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.241 Γ— 10⁹⁡(96-digit number)
92416775776463462351…66430621469028458239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.848 Γ— 10⁹⁢(97-digit number)
18483355155292692470…32861242938056916479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.696 Γ— 10⁹⁢(97-digit number)
36966710310585384940…65722485876113832959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.393 Γ— 10⁹⁢(97-digit number)
73933420621170769881…31444971752227665919
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)
14786684124234153976…62889943504455331839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.957 Γ— 10⁹⁷(98-digit number)
29573368248468307952…25779887008910663679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.914 Γ— 10⁹⁷(98-digit number)
59146736496936615904…51559774017821327359
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)
11829347299387323180…03119548035642654719
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:57,987,740 XPMΒ·at block #6,842,923 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