XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,746,451

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/13/2018, 1:02:56 AM Β· Difficulty 11.6495 Β· 4,087,324 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c563b8d7c848a7105b8f007e5d6bad7dbd93aa29710952a6420be28409adc91c
View on Chainz β†—

Height

#2,746,451

Difficulty

11.649507

Transactions

2

Size

70.67 KB

Version

2

Bits

0ba64611

Nonce

788,561,496

Timestamp

7/13/2018, 1:02:56 AM

Confirmations

4,087,324

Mined by

⛏️ P2SHATCMyxa2cmpN2u7yDwCfqciD1NLr1agCWA

Merkle Root

f1ba3f69b2b50693b1e6b1ca2a9111eea1d2ae21879c8fdb66c74df38a5daff6
Transactions (2)
Coinbase44789347582387…dd7f620ca84d39
1 in β†’ 1 out8.1100 XPM110 B
ATCMyxa2…Lr1agCWA
39a52b64f21aea…6af51dc9d49625
487 in β†’ 2 out20000.0125 XPM70.47 KB
ATCzrcjj…o1TX6nbCALPF8J52…Hjw4BMsG
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.

1.182 Γ— 10⁹⁢(97-digit number)
11827875940439497483…86551429353206850561
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
1.182 Γ— 10⁹⁢(97-digit number)
11827875940439497483…86551429353206850561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.365 Γ— 10⁹⁢(97-digit number)
23655751880878994967…73102858706413701121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.731 Γ— 10⁹⁢(97-digit number)
47311503761757989935…46205717412827402241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.462 Γ— 10⁹⁢(97-digit number)
94623007523515979871…92411434825654804481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.892 Γ— 10⁹⁷(98-digit number)
18924601504703195974…84822869651309608961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.784 Γ— 10⁹⁷(98-digit number)
37849203009406391948…69645739302619217921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.569 Γ— 10⁹⁷(98-digit number)
75698406018812783897…39291478605238435841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.513 Γ— 10⁹⁸(99-digit number)
15139681203762556779…78582957210476871681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.027 Γ— 10⁹⁸(99-digit number)
30279362407525113558…57165914420953743361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.055 Γ— 10⁹⁸(99-digit number)
60558724815050227117…14331828841907486721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.211 Γ— 10⁹⁹(100-digit number)
12111744963010045423…28663657683814973441
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:57,914,418 XPMΒ·at block #6,833,774 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