XPM Prime Explorer symbol
XPMPrime Explorer

Block #55,041

2CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/16/2013, 11:38:32 PM Β· Difficulty 8.9386 Β· 6,759,146 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b9f7926bcc6a9359a6e87e1880640e729fbd7ba7c0f13aa2875e88e01c8270cf
View on Chainz β†—

Height

#55,041

Difficulty

8.938628

Transactions

1

Size

199 B

Version

2

Bits

08f049f3

Nonce

248

Timestamp

7/16/2013, 11:38:32 PM

Confirmations

6,759,146

Mined by

⛏️ P2SHAJbz55M2Xd4eSVXFrry1sb6y1EmoHxsz79

Merkle Root

e6a10bfec16217c2b4387eabe3272b11c5478a36e036c02fca103dc340a57e21
Transactions (1)
Coinbasee6a10bfec16217…103dc340a57e21
1 in β†’ 1 out12.5000 XPM110 B
AJbz55M2…moHxsz79
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.

1.213 Γ— 10⁹²(93-digit number)
12134026028408075650…64961092275715904861
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
1.213 Γ— 10⁹²(93-digit number)
12134026028408075650…64961092275715904861
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.426 Γ— 10⁹²(93-digit number)
24268052056816151301…29922184551431809721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.853 Γ— 10⁹²(93-digit number)
48536104113632302603…59844369102863619441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.707 Γ— 10⁹²(93-digit number)
97072208227264605206…19688738205727238881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.941 Γ— 10⁹³(94-digit number)
19414441645452921041…39377476411454477761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.882 Γ— 10⁹³(94-digit number)
38828883290905842082…78754952822908955521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.765 Γ— 10⁹³(94-digit number)
77657766581811684165…57509905645817911041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.553 Γ— 10⁹⁴(95-digit number)
15531553316362336833…15019811291635822081
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:57,757,569 XPMΒ·at block #6,814,186 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