XPM Prime Explorer symbol
XPMPrime Explorer

Block #66,160

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/19/2013, 4:02:42 PM Β· Difficulty 8.9856 Β· 6,742,064 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c22d3f3fb4f1c1830549408d8d7e8fb12d2494ea3317e46e38a4c13ba8a054a6
View on Chainz β†—

Height

#66,160

Difficulty

8.985635

Transactions

2

Size

359 B

Version

2

Bits

08fc528f

Nonce

22

Timestamp

7/19/2013, 4:02:42 PM

Confirmations

6,742,064

Mined by

⛏️ P2SHAGSNtSisYBYroK1NsxfEvQMQuUTkNJmCfG

Merkle Root

ebb995191cb9b3fda3b7043117bcad9dceb87e638c7ec10ec2d0340451654d9b
Transactions (2)
Coinbase591c33e7c0000c…ac27283a956503
1 in β†’ 1 out12.3800 XPM110 B
AGSNtSis…TkNJmCfG
fb6118fec0bb52…64e5442e9f8030
1 in β†’ 1 out12.4000 XPM159 B
AKubZ5rY…L6ewHYWc
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.

4.623 Γ— 10⁹⁴(95-digit number)
46231439315781965156…84876822409451795349
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
4.623 Γ— 10⁹⁴(95-digit number)
46231439315781965156…84876822409451795349
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
9.246 Γ— 10⁹⁴(95-digit number)
92462878631563930312…69753644818903590699
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.849 Γ— 10⁹⁡(96-digit number)
18492575726312786062…39507289637807181399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.698 Γ— 10⁹⁡(96-digit number)
36985151452625572125…79014579275614362799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.397 Γ— 10⁹⁡(96-digit number)
73970302905251144250…58029158551228725599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.479 Γ— 10⁹⁢(97-digit number)
14794060581050228850…16058317102457451199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.958 Γ— 10⁹⁢(97-digit number)
29588121162100457700…32116634204914902399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.917 Γ— 10⁹⁢(97-digit number)
59176242324200915400…64233268409829804799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.183 Γ— 10⁹⁷(98-digit number)
11835248464840183080…28466536819659609599
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:57,709,844 XPMΒ·at block #6,808,223 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.
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