XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,636,290

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/29/2018, 12:55:47 PM Β· Difficulty 11.3733 Β· 4,203,845 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
adb7cd2c06eee450fe13494b32ae6b36953bb9c6e1f08906c30a0dd3b690816e
View on Chainz β†—

Height

#2,636,290

Difficulty

11.373328

Transactions

1

Size

200 B

Version

2

Bits

0b5f9274

Nonce

850,505,487

Timestamp

4/29/2018, 12:55:47 PM

Confirmations

4,203,845

Mined by

⛏️ P2SHARE1GUod3UzFnsf4E6gdMGmgs7wrsMP8bJ

Merkle Root

bd5dc66e3825b3f0f271b5193ea014226652ae43007d61268163a791832e3708
Transactions (1)
Coinbasebd5dc66e3825b3…63a791832e3708
1 in β†’ 1 out7.7200 XPM110 B
ARE1GUod…wrsMP8bJ
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.

1.967 Γ— 10⁹⁡(96-digit number)
19673074188764622014…34833809280447947521
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
1.967 Γ— 10⁹⁡(96-digit number)
19673074188764622014…34833809280447947521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.934 Γ— 10⁹⁡(96-digit number)
39346148377529244028…69667618560895895041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.869 Γ— 10⁹⁡(96-digit number)
78692296755058488057…39335237121791790081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.573 Γ— 10⁹⁢(97-digit number)
15738459351011697611…78670474243583580161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.147 Γ— 10⁹⁢(97-digit number)
31476918702023395223…57340948487167160321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.295 Γ— 10⁹⁢(97-digit number)
62953837404046790446…14681896974334320641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.259 Γ— 10⁹⁷(98-digit number)
12590767480809358089…29363793948668641281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.518 Γ— 10⁹⁷(98-digit number)
25181534961618716178…58727587897337282561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.036 Γ— 10⁹⁷(98-digit number)
50363069923237432356…17455175794674565121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.007 Γ— 10⁹⁸(99-digit number)
10072613984647486471…34910351589349130241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.014 Γ— 10⁹⁸(99-digit number)
20145227969294972942…69820703178698260481
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,965,395 XPMΒ·at block #6,840,134 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