XPM Prime Explorer symbol
XPMPrime Explorer

Block #1,682,107

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/20/2016, 6:50:21 PM Β· Difficulty 10.7185 Β· 5,151,866 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
aa2c0c84e90653ba4118b1ecf46bd990682f981f43006528211b4a6211fbe22f
View on Chainz β†—

Height

#1,682,107

Difficulty

10.718534

Transactions

1

Size

243 B

Version

2

Bits

0ab7f1d4

Nonce

1,719,559,774

Timestamp

7/20/2016, 6:50:21 PM

Confirmations

5,151,866

Mined by

⛏️ P2SHAJgZBh3x4MUdHjG3qq81iJgboZ9DpUcwi5

Merkle Root

5e1f0decf34c8ba487b99a829c13a90dd0911289814f0bb79ce7bc4a7730e7d3
Transactions (1)
Coinbase5e1f0decf34c8b…e7bc4a7730e7d3
1 in β†’ 2 out8.6900 XPM152 B
AJgZBh3x…9DpUcwi5ALPu3s2c…EJXLjVFh
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.

8.894 Γ— 10⁹⁡(96-digit number)
88945987020319785319…43497926381553804561
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
8.894 Γ— 10⁹⁡(96-digit number)
88945987020319785319…43497926381553804561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.778 Γ— 10⁹⁢(97-digit number)
17789197404063957063…86995852763107609121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.557 Γ— 10⁹⁢(97-digit number)
35578394808127914127…73991705526215218241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.115 Γ— 10⁹⁢(97-digit number)
71156789616255828255…47983411052430436481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.423 Γ— 10⁹⁷(98-digit number)
14231357923251165651…95966822104860872961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.846 Γ— 10⁹⁷(98-digit number)
28462715846502331302…91933644209721745921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.692 Γ— 10⁹⁷(98-digit number)
56925431693004662604…83867288419443491841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.138 Γ— 10⁹⁸(99-digit number)
11385086338600932520…67734576838886983681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.277 Γ— 10⁹⁸(99-digit number)
22770172677201865041…35469153677773967361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.554 Γ— 10⁹⁸(99-digit number)
45540345354403730083…70938307355547934721
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:57,916,007 XPMΒ·at block #6,833,972 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