XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,636,058

1CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the First Kind Β· Discovered 4/29/2018, 11:00:41 AM Β· Difficulty 11.3584 Β· 4,206,731 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
79d4d63f728580970ded1f328de208c3d7686d489f17f504c41c03a305811044
View on Chainz β†—

Height

#2,636,058

Difficulty

11.358426

Transactions

2

Size

3.30 KB

Version

2

Bits

0b5bc1c7

Nonce

465,599,442

Timestamp

4/29/2018, 11:00:41 AM

Confirmations

4,206,731

Mined by

⛏️ P2SHAUVX9pBM5ZC2utME7wMTuRUnMt1CSFEdaC

Merkle Root

88086cc46f5e607bca65d4d4e02ee8683a7db9e0d2528f0a2eb22b53bd03ab9e
Transactions (2)
Coinbase51cac38c982c05…a68b478695cba6
1 in β†’ 1 out7.7800 XPM110 B
AUVX9pBM…1CSFEdaC
d9738eb1270f47…802a7e83460536
21 in β†’ 2 out200.9500 XPM3.11 KB
APK9JojF…SYBSmzEbAGbdrG7b…6HsoJoDt
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.

2.708 Γ— 10⁹⁡(96-digit number)
27080825296756004215…67293582921800798719
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
2.708 Γ— 10⁹⁡(96-digit number)
27080825296756004215…67293582921800798719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.416 Γ— 10⁹⁡(96-digit number)
54161650593512008430…34587165843601597439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.083 Γ— 10⁹⁢(97-digit number)
10832330118702401686…69174331687203194879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.166 Γ— 10⁹⁢(97-digit number)
21664660237404803372…38348663374406389759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.332 Γ— 10⁹⁢(97-digit number)
43329320474809606744…76697326748812779519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.665 Γ— 10⁹⁢(97-digit number)
86658640949619213489…53394653497625559039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.733 Γ— 10⁹⁷(98-digit number)
17331728189923842697…06789306995251118079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.466 Γ— 10⁹⁷(98-digit number)
34663456379847685395…13578613990502236159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.932 Γ— 10⁹⁷(98-digit number)
69326912759695370791…27157227981004472319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.386 Γ— 10⁹⁸(99-digit number)
13865382551939074158…54314455962008944639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.773 Γ— 10⁹⁸(99-digit number)
27730765103878148316…08628911924017889279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
12
2^11 Γ— origin βˆ’ 1
5.546 Γ— 10⁹⁸(99-digit number)
55461530207756296633…17257823848035778559
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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:57,986,650 XPMΒ·at block #6,842,788 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