XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,314,574

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/29/2017, 5:49:53 PM Β· Difficulty 10.9068 Β· 4,512,147 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e61b968e6566ba348a32c79668156eb7ece0535a85a60b1c5760897ee05f3bc1
View on Chainz β†—

Height

#2,314,574

Difficulty

10.906834

Transactions

2

Size

541 B

Version

2

Bits

0ae82648

Nonce

1,518,305,979

Timestamp

9/29/2017, 5:49:53 PM

Confirmations

4,512,147

Mined by

⛏️ P2SHASmsJ7VyhWraBrgBHbfzFw2oKJC7qTnPKC

Merkle Root

a6f9b89162bcca3c2ea154292ffc48ed0597f532c38af5645a6f827c47094db7
Transactions (2)
Coinbase73fdaadfcf5f9b…91ee483f90f8e4
1 in β†’ 1 out8.4000 XPM110 B
ASmsJ7Vy…C7qTnPKC
f984a6bc6e958a…7fb38226b3af3c
2 in β†’ 1 out2499.9900 XPM341 B
AcxhUhX6…N8N8w2tm
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.

6.218 Γ— 10⁹⁴(95-digit number)
62184154687273035307…89863305873686196481
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
6.218 Γ— 10⁹⁴(95-digit number)
62184154687273035307…89863305873686196481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.243 Γ— 10⁹⁡(96-digit number)
12436830937454607061…79726611747372392961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.487 Γ— 10⁹⁡(96-digit number)
24873661874909214122…59453223494744785921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.974 Γ— 10⁹⁡(96-digit number)
49747323749818428245…18906446989489571841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.949 Γ— 10⁹⁡(96-digit number)
99494647499636856491…37812893978979143681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.989 Γ— 10⁹⁢(97-digit number)
19898929499927371298…75625787957958287361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.979 Γ— 10⁹⁢(97-digit number)
39797858999854742596…51251575915916574721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.959 Γ— 10⁹⁢(97-digit number)
79595717999709485193…02503151831833149441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.591 Γ— 10⁹⁷(98-digit number)
15919143599941897038…05006303663666298881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.183 Γ— 10⁹⁷(98-digit number)
31838287199883794077…10012607327332597761
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:57,857,922 XPMΒ·at block #6,826,720 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