XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,280,060

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/3/2017, 1:28:29 AM Β· Difficulty 10.9563 Β· 4,562,864 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6b11fd275b102516c396ef0a5d7d8ee188bbd7adab1d98a767f45124dca86e20
View on Chainz β†—

Height

#2,280,060

Difficulty

10.956280

Transactions

1

Size

200 B

Version

2

Bits

0af4cec9

Nonce

719,501,809

Timestamp

9/3/2017, 1:28:29 AM

Confirmations

4,562,864

Mined by

⛏️ P2SHALY32zDThdxiRzvbGSknYtNyF2xd5VKZR6

Merkle Root

cfa9de4affcda8627b6aab70c10a2d2aae695d2e111486a555203abfd4f4fc9e
Transactions (1)
Coinbasecfa9de4affcda8…203abfd4f4fc9e
1 in β†’ 1 out8.3200 XPM110 B
ALY32zDT…xd5VKZR6
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.

1.340 Γ— 10⁹⁴(95-digit number)
13401975368410099811…04272839013863574401
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
1.340 Γ— 10⁹⁴(95-digit number)
13401975368410099811…04272839013863574401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.680 Γ— 10⁹⁴(95-digit number)
26803950736820199622…08545678027727148801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.360 Γ— 10⁹⁴(95-digit number)
53607901473640399245…17091356055454297601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.072 Γ— 10⁹⁡(96-digit number)
10721580294728079849…34182712110908595201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.144 Γ— 10⁹⁡(96-digit number)
21443160589456159698…68365424221817190401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.288 Γ— 10⁹⁡(96-digit number)
42886321178912319396…36730848443634380801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.577 Γ— 10⁹⁡(96-digit number)
85772642357824638792…73461696887268761601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.715 Γ— 10⁹⁢(97-digit number)
17154528471564927758…46923393774537523201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.430 Γ— 10⁹⁢(97-digit number)
34309056943129855517…93846787549075046401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.861 Γ— 10⁹⁢(97-digit number)
68618113886259711034…87693575098150092801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.372 Γ— 10⁹⁷(98-digit number)
13723622777251942206…75387150196300185601
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Cunningham Chain of the Second 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,987,740 XPMΒ·at block #6,842,923 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