XPM Prime Explorer symbol
XPMPrime Explorer

Block #439,606

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/11/2014, 7:32:30 PM Β· Difficulty 10.3601 Β· 6,370,963 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1061889442558a445639a5bc9b6b667862d3f63cd45f25f75686db30badd507c
View on Chainz β†—

Height

#439,606

Difficulty

10.360058

Transactions

2

Size

986 B

Version

2

Bits

0a5c2cc5

Nonce

36,904

Timestamp

3/11/2014, 7:32:30 PM

Confirmations

6,370,963

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

03d9b2d3637ec07b5f6123ca24bdd578b82ea82ac7a6af3c113b4e4ad37e7529
Transactions (2)
Coinbase112497f478a05f…677000ff8f3a9f
1 in β†’ 1 out9.3152 XPM110 B
AeKNrjNj…1NEq95Ta
6a6f84716ac193…22e64929bfc757
5 in β†’ 1 out4.0000 XPM786 B
Ab7gQN4B…tnPehPRf
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.

9.342 Γ— 10⁹⁴(95-digit number)
93421787254261808159…20533651778397619319
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
9.342 Γ— 10⁹⁴(95-digit number)
93421787254261808159…20533651778397619319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.868 Γ— 10⁹⁡(96-digit number)
18684357450852361631…41067303556795238639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.736 Γ— 10⁹⁡(96-digit number)
37368714901704723263…82134607113590477279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.473 Γ— 10⁹⁡(96-digit number)
74737429803409446527…64269214227180954559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.494 Γ— 10⁹⁢(97-digit number)
14947485960681889305…28538428454361909119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.989 Γ— 10⁹⁢(97-digit number)
29894971921363778611…57076856908723818239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.978 Γ— 10⁹⁢(97-digit number)
59789943842727557222…14153713817447636479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.195 Γ— 10⁹⁷(98-digit number)
11957988768545511444…28307427634895272959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.391 Γ— 10⁹⁷(98-digit number)
23915977537091022888…56614855269790545919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.783 Γ— 10⁹⁷(98-digit number)
47831955074182045777…13229710539581091839
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,728,643 XPMΒ·at block #6,810,568 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