XPM Prime Explorer symbol
XPMPrime Explorer

Block #41,875

2CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/14/2013, 5:27:46 PM Β· Difficulty 8.5598 Β· 6,775,920 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
1dba3a9ec893afaf965223a34f3d3bfcf1a7439261a16c44db3e3337b244f219
View on Chainz β†—

Height

#41,875

Difficulty

8.559819

Transactions

1

Size

197 B

Version

2

Bits

088f5054

Nonce

823

Timestamp

7/14/2013, 5:27:46 PM

Confirmations

6,775,920

Mined by

⛏️ P2SHAcz8aGVgQtomPv8VR1HBsHZ8EFJhGrr8ay

Merkle Root

e2a7b6726c2926d865c2b5740915da94cefa80ac3071fa021b1ca0164d30ec86
Transactions (1)
Coinbasee2a7b6726c2926…1ca0164d30ec86
1 in β†’ 1 out13.6300 XPM110 B
Acz8aGVg…JhGrr8ay
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.

3.483 Γ— 10⁸⁷(88-digit number)
34831503267912901824…50601097860083082631
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
3.483 Γ— 10⁸⁷(88-digit number)
34831503267912901824…50601097860083082631
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.966 Γ— 10⁸⁷(88-digit number)
69663006535825803649…01202195720166165261
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.393 Γ— 10⁸⁸(89-digit number)
13932601307165160729…02404391440332330521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.786 Γ— 10⁸⁸(89-digit number)
27865202614330321459…04808782880664661041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.573 Γ— 10⁸⁸(89-digit number)
55730405228660642919…09617565761329322081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.114 Γ— 10⁸⁹(90-digit number)
11146081045732128583…19235131522658644161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.229 Γ— 10⁸⁹(90-digit number)
22292162091464257167…38470263045317288321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.458 Γ— 10⁸⁹(90-digit number)
44584324182928514335…76940526090634576641
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 8 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
CommonChain length 8

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,786,420 XPMΒ·at block #6,817,794 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