XPM Prime Explorer symbol
XPMPrime Explorer

Block #411,817

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 2/20/2014, 2:39:58 AM Β· Difficulty 10.4165 Β· 6,403,235 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
6907270f21c33d2faadc75823e085cec041cf73ab200528f439c95429acc86be
View on Chainz β†—

Height

#411,817

Difficulty

10.416513

Transactions

1

Size

936 B

Version

2

Bits

0a6aa097

Nonce

62,904

Timestamp

2/20/2014, 2:39:58 AM

Confirmations

6,403,235

Mined by

⛏️ HaSjAQwRN8bEjE7sawFBq7N38V9niAV8PsTcY9

Merkle Root

7f62912aa4ae9263182cb7532a4a0f94e6e2daf644635f5cc7a2bb2b833683c4
Transactions (1)
Coinbase7f62912aa4ae92…a2bb2b833683c4
1 in β†’ 23 out9.2000 XPM845 B
AQwRN8bE…V8PsTcY9Aac9Hjdg…P4ktypc3AGQxR1oS…2N1xAZXNAPAdzfu9…nv4DjCYAAGKhfQo2…h7fBXLX6
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.

3.691 Γ— 10⁹⁢(97-digit number)
36917311728567701263…39295009311367113689
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
3.691 Γ— 10⁹⁢(97-digit number)
36917311728567701263…39295009311367113689
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.383 Γ— 10⁹⁢(97-digit number)
73834623457135402526…78590018622734227379
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.476 Γ— 10⁹⁷(98-digit number)
14766924691427080505…57180037245468454759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.953 Γ— 10⁹⁷(98-digit number)
29533849382854161010…14360074490936909519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.906 Γ— 10⁹⁷(98-digit number)
59067698765708322020…28720148981873819039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.181 Γ— 10⁹⁸(99-digit number)
11813539753141664404…57440297963747638079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.362 Γ— 10⁹⁸(99-digit number)
23627079506283328808…14880595927495276159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.725 Γ— 10⁹⁸(99-digit number)
47254159012566657616…29761191854990552319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.450 Γ— 10⁹⁸(99-digit number)
94508318025133315233…59522383709981104639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.890 Γ— 10⁹⁹(100-digit number)
18901663605026663046…19044767419962209279
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:57,764,507 XPMΒ·at block #6,815,051 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