XPM Prime Explorer symbol
XPMPrime Explorer

Block #1,441,330

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 2/3/2016, 9:05:35 PM Β· Difficulty 10.7623 Β· 5,401,667 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e17188dbbdccf938452ee032cdf0316f3b6660cbfdf24e23dfc4a460f4a0440d
View on Chainz β†—

Height

#1,441,330

Difficulty

10.762296

Transactions

1

Size

199 B

Version

2

Bits

0ac325d8

Nonce

1,226,423,352

Timestamp

2/3/2016, 9:05:35 PM

Confirmations

5,401,667

Mined by

⛏️ P2SHAZCf5KBZK6L2jGkhkWMa5xEMkEahfhvPhp

Merkle Root

1031bf345a0de21d351c94d7bae07cccf0dc8643d2be7886c737014053f309a8
Transactions (1)
Coinbase1031bf345a0de2…37014053f309a8
1 in β†’ 1 out8.6200 XPM109 B
AZCf5KBZ…ahfhvPhp
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.

9.286 Γ— 10⁹³(94-digit number)
92869399796233689374…38111737055392773159
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
9.286 Γ— 10⁹³(94-digit number)
92869399796233689374…38111737055392773159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.857 Γ— 10⁹⁴(95-digit number)
18573879959246737874…76223474110785546319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.714 Γ— 10⁹⁴(95-digit number)
37147759918493475749…52446948221571092639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.429 Γ— 10⁹⁴(95-digit number)
74295519836986951499…04893896443142185279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.485 Γ— 10⁹⁡(96-digit number)
14859103967397390299…09787792886284370559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.971 Γ— 10⁹⁡(96-digit number)
29718207934794780599…19575585772568741119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.943 Γ— 10⁹⁡(96-digit number)
59436415869589561199…39151171545137482239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.188 Γ— 10⁹⁢(97-digit number)
11887283173917912239…78302343090274964479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.377 Γ— 10⁹⁢(97-digit number)
23774566347835824479…56604686180549928959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.754 Γ— 10⁹⁢(97-digit number)
47549132695671648959…13209372361099857919
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:57,988,331 XPMΒ·at block #6,842,996 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