XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,262,438

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/22/2017, 2:26:39 AM Β· Difficulty 10.9521 Β· 4,571,564 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c8ebc7983a4ea68d06f23b275069a0a46c07cd55e3d464d03a61e3abf312affe
View on Chainz β†—

Height

#2,262,438

Difficulty

10.952116

Transactions

2

Size

869 B

Version

2

Bits

0af3bde5

Nonce

1,213,229,056

Timestamp

8/22/2017, 2:26:39 AM

Confirmations

4,571,564

Mined by

⛏️ P2SHAW1133tvuhBAoFb9HVYaMCDMV1uPPGJQ4T

Merkle Root

d8f0d69a3e1c871312f13e63528ea15ba691b0daf823146596fb75c227ea6480
Transactions (2)
Coinbaseb61ac87e6f6b6c…918422e16fb1c7
1 in β†’ 1 out8.3300 XPM110 B
AW1133tv…uPPGJQ4T
966b4deecf3b62…eb25130d9fc7d6
4 in β†’ 2 out24.2685 XPM669 B
AU5bsQFi…RA19fWTBATHn4Cxc…1t2uZDYY
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.

1.282 Γ— 10⁹⁡(96-digit number)
12820053711616086408…48919178615268286081
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
1.282 Γ— 10⁹⁡(96-digit number)
12820053711616086408…48919178615268286081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.564 Γ— 10⁹⁡(96-digit number)
25640107423232172816…97838357230536572161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.128 Γ— 10⁹⁡(96-digit number)
51280214846464345633…95676714461073144321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.025 Γ— 10⁹⁢(97-digit number)
10256042969292869126…91353428922146288641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.051 Γ— 10⁹⁢(97-digit number)
20512085938585738253…82706857844292577281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.102 Γ— 10⁹⁢(97-digit number)
41024171877171476507…65413715688585154561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.204 Γ— 10⁹⁢(97-digit number)
82048343754342953014…30827431377170309121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.640 Γ— 10⁹⁷(98-digit number)
16409668750868590602…61654862754340618241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.281 Γ— 10⁹⁷(98-digit number)
32819337501737181205…23309725508681236481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.563 Γ— 10⁹⁷(98-digit number)
65638675003474362411…46619451017362472961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.312 Γ— 10⁹⁸(99-digit number)
13127735000694872482…93238902034724945921
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:57,916,243 XPMΒ·at block #6,834,001 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