XPM Prime Explorer symbol
XPMPrime Explorer

Block #139,492

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/29/2013, 12:58:39 AM Β· Difficulty 9.8316 Β· 6,669,987 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b8827432b3212f40848be33e6c8499f8ef2fdc801e4189c788bc2e2660e6eb37
View on Chainz β†—

Height

#139,492

Difficulty

9.831637

Transactions

2

Size

814 B

Version

2

Bits

09d4e625

Nonce

22,005

Timestamp

8/29/2013, 12:58:39 AM

Confirmations

6,669,987

Mined by

⛏️ P2SHAN7XEitUUuigurw1EkSj72AqF71M2iWp4h

Merkle Root

f39ca84ea740c37fbec4b73a0e83f6ad2e8a5e287d9bf58516f8f2b0f2397bab
Transactions (2)
Coinbase4ddfafe6de6077…38891807e3d2aa
1 in β†’ 1 out10.3400 XPM109 B
AN7XEitU…1M2iWp4h
1ba3770c1bf207…6a3cfb58b0b205
5 in β†’ 1 out51.9500 XPM615 B
AV6URp9C…SYeCgYBK
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.

7.039 Γ— 10⁹⁴(95-digit number)
70390921058815541672…02589692712770511359
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
7.039 Γ— 10⁹⁴(95-digit number)
70390921058815541672…02589692712770511359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.407 Γ— 10⁹⁡(96-digit number)
14078184211763108334…05179385425541022719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.815 Γ— 10⁹⁡(96-digit number)
28156368423526216669…10358770851082045439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.631 Γ— 10⁹⁡(96-digit number)
56312736847052433338…20717541702164090879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.126 Γ— 10⁹⁢(97-digit number)
11262547369410486667…41435083404328181759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.252 Γ— 10⁹⁢(97-digit number)
22525094738820973335…82870166808656363519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.505 Γ— 10⁹⁢(97-digit number)
45050189477641946670…65740333617312727039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.010 Γ— 10⁹⁢(97-digit number)
90100378955283893340…31480667234625454079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.802 Γ— 10⁹⁷(98-digit number)
18020075791056778668…62961334469250908159
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:57,719,902 XPMΒ·at block #6,809,478 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