XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,207,643

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/15/2017, 9:39:15 AM Β· Difficulty 10.9454 Β· 4,635,456 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
9d2954c9303ecfdac78caf9d986646db4b85bcb994d6669341e30bbb28582acf
View on Chainz β†—

Height

#2,207,643

Difficulty

10.945352

Transactions

1

Size

201 B

Version

2

Bits

0af20293

Nonce

210,838,950

Timestamp

7/15/2017, 9:39:15 AM

Confirmations

4,635,456

Mined by

⛏️ P2SHAN7ttpuYQ5RvFKtEf3VGt9rGhueTEa5syw

Merkle Root

21152c77baf047cf601f7fbeeae92bc7c651482b23895afa5f7f5121abe61ee0
Transactions (1)
Coinbase21152c77baf047…7f5121abe61ee0
1 in β†’ 1 out8.3300 XPM110 B
AN7ttpuY…eTEa5syw
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.

1.742 Γ— 10⁹⁢(97-digit number)
17423683171063241531…65639406771325552641
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
1.742 Γ— 10⁹⁢(97-digit number)
17423683171063241531…65639406771325552641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.484 Γ— 10⁹⁢(97-digit number)
34847366342126483063…31278813542651105281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.969 Γ— 10⁹⁢(97-digit number)
69694732684252966127…62557627085302210561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.393 Γ— 10⁹⁷(98-digit number)
13938946536850593225…25115254170604421121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.787 Γ— 10⁹⁷(98-digit number)
27877893073701186451…50230508341208842241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.575 Γ— 10⁹⁷(98-digit number)
55755786147402372902…00461016682417684481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.115 Γ— 10⁹⁸(99-digit number)
11151157229480474580…00922033364835368961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.230 Γ— 10⁹⁸(99-digit number)
22302314458960949160…01844066729670737921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.460 Γ— 10⁹⁸(99-digit number)
44604628917921898321…03688133459341475841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
8.920 Γ— 10⁹⁸(99-digit number)
89209257835843796643…07376266918682951681
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:57,989,155 XPMΒ·at block #6,843,098 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