XPM Prime Explorer symbol
XPMPrime Explorer

Block #87,253

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/28/2013, 6:22:29 PM Β· Difficulty 9.2778 Β· 6,727,224 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
240d0dbd326aaf226bf1ec38040a77fca019bf60a7d1e3e9a8463ce2794f0796
View on Chainz β†—

Height

#87,253

Difficulty

9.277794

Transactions

1

Size

198 B

Version

2

Bits

09471d83

Nonce

177

Timestamp

7/28/2013, 6:22:29 PM

Confirmations

6,727,224

Mined by

⛏️ P2SHAXPy6qfAWqb7XLVCUpW6irQwxeHTAhrhpM

Merkle Root

ede895c23ddf576285469b3565ec0af9df7ce646912af8d83e435bb480319713
Transactions (1)
Coinbaseede895c23ddf57…435bb480319713
1 in β†’ 1 out11.6000 XPM110 B
AXPy6qfA…HTAhrhpM
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.

3.387 Γ— 10⁸⁸(89-digit number)
33870216480751376592…59554710446146621949
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
3.387 Γ— 10⁸⁸(89-digit number)
33870216480751376592…59554710446146621949
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.774 Γ— 10⁸⁸(89-digit number)
67740432961502753184…19109420892293243899
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.354 Γ— 10⁸⁹(90-digit number)
13548086592300550636…38218841784586487799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.709 Γ— 10⁸⁹(90-digit number)
27096173184601101273…76437683569172975599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.419 Γ— 10⁸⁹(90-digit number)
54192346369202202547…52875367138345951199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.083 Γ— 10⁹⁰(91-digit number)
10838469273840440509…05750734276691902399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.167 Γ— 10⁹⁰(91-digit number)
21676938547680881019…11501468553383804799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.335 Γ— 10⁹⁰(91-digit number)
43353877095361762038…23002937106767609599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.670 Γ— 10⁹⁰(91-digit number)
86707754190723524076…46005874213535219199
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,759,891 XPMΒ·at block #6,814,476 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