XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,802,197

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/20/2018, 1:25:20 PM Β· Difficulty 11.6707 Β· 4,037,635 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e2a9c8e957d68da61e4b92b666c792a56aa8ceab4adb305b264a7fabc81ffbd8
View on Chainz β†—

Height

#2,802,197

Difficulty

11.670652

Transactions

2

Size

21.96 KB

Version

2

Bits

0babafe0

Nonce

1,842,324,907

Timestamp

8/20/2018, 1:25:20 PM

Confirmations

4,037,635

Mined by

⛏️ P2SHARFyyo5RBt9UVbWzkDdmAQuU76fjHuU2uX

Merkle Root

052e2bc6d9823718bda2d54bc7a9705e56b59b495aa1556f102540d1cba835e9
Transactions (2)
Coinbase38df22df572c02…5d0b3c562a640f
1 in β†’ 1 out7.5600 XPM109 B
ARFyyo5R…fjHuU2uX
9ce7120ea2aa30…300991409e2169
150 in β†’ 2 out1490.4500 XPM21.77 KB
ARiS2nqo…pJnUrAHJALh5G3Np…6TsNC2wj
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.

1.127 Γ— 10⁹⁴(95-digit number)
11273167601674884571…40757380576361406801
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
1.127 Γ— 10⁹⁴(95-digit number)
11273167601674884571…40757380576361406801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.254 Γ— 10⁹⁴(95-digit number)
22546335203349769143…81514761152722813601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.509 Γ— 10⁹⁴(95-digit number)
45092670406699538286…63029522305445627201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.018 Γ— 10⁹⁴(95-digit number)
90185340813399076573…26059044610891254401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.803 Γ— 10⁹⁡(96-digit number)
18037068162679815314…52118089221782508801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.607 Γ— 10⁹⁡(96-digit number)
36074136325359630629…04236178443565017601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.214 Γ— 10⁹⁡(96-digit number)
72148272650719261258…08472356887130035201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.442 Γ— 10⁹⁢(97-digit number)
14429654530143852251…16944713774260070401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.885 Γ— 10⁹⁢(97-digit number)
28859309060287704503…33889427548520140801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.771 Γ— 10⁹⁢(97-digit number)
57718618120575409007…67778855097040281601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.154 Γ— 10⁹⁷(98-digit number)
11543723624115081801…35557710194080563201
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:57,962,953 XPMΒ·at block #6,839,831 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