XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,051,479

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/3/2017, 1:06:36 PM Β· Difficulty 10.7151 Β· 4,788,017 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
9f68202b63762bc1092fc9d54fa87f2d3f23ccb7921cf8389548ec8e6adf89db
View on Chainz β†—

Height

#2,051,479

Difficulty

10.715054

Transactions

1

Size

200 B

Version

2

Bits

0ab70dca

Nonce

60,962,658

Timestamp

4/3/2017, 1:06:36 PM

Confirmations

4,788,017

Mined by

⛏️ P2SHATU4fzt8K5okw5Mg5xD7VJ8UGgCEyeRrMK

Merkle Root

8c02cc4916e4ed5b495127e90794d3e4e79fc16124702d53f30b546accad7010
Transactions (1)
Coinbase8c02cc4916e4ed…0b546accad7010
1 in β†’ 1 out8.7000 XPM109 B
ATU4fzt8…CEyeRrMK
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.

1.274 Γ— 10⁹⁷(98-digit number)
12741930851970210908…80398782511320862721
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
1.274 Γ— 10⁹⁷(98-digit number)
12741930851970210908…80398782511320862721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.548 Γ— 10⁹⁷(98-digit number)
25483861703940421816…60797565022641725441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.096 Γ— 10⁹⁷(98-digit number)
50967723407880843632…21595130045283450881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.019 Γ— 10⁹⁸(99-digit number)
10193544681576168726…43190260090566901761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.038 Γ— 10⁹⁸(99-digit number)
20387089363152337453…86380520181133803521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.077 Γ— 10⁹⁸(99-digit number)
40774178726304674906…72761040362267607041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.154 Γ— 10⁹⁸(99-digit number)
81548357452609349812…45522080724535214081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.630 Γ— 10⁹⁹(100-digit number)
16309671490521869962…91044161449070428161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.261 Γ— 10⁹⁹(100-digit number)
32619342981043739925…82088322898140856321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.523 Γ— 10⁹⁹(100-digit number)
65238685962087479850…64176645796281712641
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:57,960,264 XPMΒ·at block #6,839,495 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