XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,152,490

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/9/2017, 1:33:40 AM Β· Difficulty 10.9018 Β· 4,689,419 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
539cab1ab98aefa8db3ece33426f1b793da5d8d31c43a1020f90f1e4ac274988
View on Chainz β†—

Height

#2,152,490

Difficulty

10.901790

Transactions

2

Size

427 B

Version

2

Bits

0ae6dbbd

Nonce

1,724,787,627

Timestamp

6/9/2017, 1:33:40 AM

Confirmations

4,689,419

Mined by

⛏️ P2SHAUYkiCLeS3fj6rGUNvL52Gg6vT8ozyu85K

Merkle Root

516afed2d748bdc04ce3b95d1cc41976b406e3502289aac68c3c1056ceaebcbf
Transactions (2)
Coinbaseef88429691a7d1…3b94949d76eec3
1 in β†’ 1 out8.4100 XPM110 B
AUYkiCLe…8ozyu85K
4ac051b08a1fbe…85471761d7e5db
1 in β†’ 2 out9861.0741 XPM227 B
AcSguLq7…v9WmRoRrAV6GVuy1…YKkdVbyz
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.

9.605 Γ— 10⁹³(94-digit number)
96051195930418700200…83760716680858045441
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
9.605 Γ— 10⁹³(94-digit number)
96051195930418700200…83760716680858045441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.921 Γ— 10⁹⁴(95-digit number)
19210239186083740040…67521433361716090881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.842 Γ— 10⁹⁴(95-digit number)
38420478372167480080…35042866723432181761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.684 Γ— 10⁹⁴(95-digit number)
76840956744334960160…70085733446864363521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.536 Γ— 10⁹⁡(96-digit number)
15368191348866992032…40171466893728727041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.073 Γ— 10⁹⁡(96-digit number)
30736382697733984064…80342933787457454081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.147 Γ— 10⁹⁡(96-digit number)
61472765395467968128…60685867574914908161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.229 Γ— 10⁹⁢(97-digit number)
12294553079093593625…21371735149829816321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.458 Γ— 10⁹⁢(97-digit number)
24589106158187187251…42743470299659632641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.917 Γ— 10⁹⁢(97-digit number)
49178212316374374502…85486940599319265281
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 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
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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,979,647 XPMΒ·at block #6,841,908 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