XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,507,315

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 2/5/2018, 4:46:02 PM Β· Difficulty 10.9791 Β· 4,334,763 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8851f18987708fed99fca4de835a8fa3b0d7dcf928a93a77ee4e9c712e26d936
View on Chainz β†—

Height

#2,507,315

Difficulty

10.979120

Transactions

2

Size

870 B

Version

2

Bits

0afaa7a2

Nonce

258,853,362

Timestamp

2/5/2018, 4:46:02 PM

Confirmations

4,334,763

Mined by

⛏️ P2SHALLfrczRRHukByc9nf1p4P9gRgvi68ZR4w

Merkle Root

7aa4fb02ba64458b6b4307ff8844a4ce08f419df5110a6b51425a5ae64404938
Transactions (2)
Coinbase63f195c62ce052…52725fcd7cf984
1 in β†’ 1 out8.2900 XPM109 B
ALLfrczR…vi68ZR4w
688df8c4d907e5…023e7a6e2be992
4 in β†’ 2 out696.3158 XPM671 B
AGKgZU8e…Fc9q1A13AeDNi8ix…oHN4A6mc
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.

8.935 Γ— 10⁹³(94-digit number)
89351381940639870663…12142136082942852561
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
8.935 Γ— 10⁹³(94-digit number)
89351381940639870663…12142136082942852561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.787 Γ— 10⁹⁴(95-digit number)
17870276388127974132…24284272165885705121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.574 Γ— 10⁹⁴(95-digit number)
35740552776255948265…48568544331771410241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.148 Γ— 10⁹⁴(95-digit number)
71481105552511896530…97137088663542820481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.429 Γ— 10⁹⁡(96-digit number)
14296221110502379306…94274177327085640961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.859 Γ— 10⁹⁡(96-digit number)
28592442221004758612…88548354654171281921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.718 Γ— 10⁹⁡(96-digit number)
57184884442009517224…77096709308342563841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.143 Γ— 10⁹⁢(97-digit number)
11436976888401903444…54193418616685127681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.287 Γ— 10⁹⁢(97-digit number)
22873953776803806889…08386837233370255361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.574 Γ— 10⁹⁢(97-digit number)
45747907553607613779…16773674466740510721
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:57,981,008 XPMΒ·at block #6,842,077 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