XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,051,506

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/3/2017, 1:16:10 PM Β· Difficulty 10.7161 Β· 4,792,322 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2c09e9122825223e648eae1737715fd7fff2dc006aca6f869aa2d2aa75692054
View on Chainz β†—

Height

#2,051,506

Difficulty

10.716074

Transactions

1

Size

199 B

Version

2

Bits

0ab750a6

Nonce

250,715,999

Timestamp

4/3/2017, 1:16:10 PM

Confirmations

4,792,322

Mined by

⛏️ P2SHARFLbJc1tN3dcc49dCi5BpiZJUe393PV1Y

Merkle Root

f230b4a7294743e3a6553850c298e6637f1b2ab5aaa7be34971c7fdc342e4ba9
Transactions (1)
Coinbasef230b4a7294743…1c7fdc342e4ba9
1 in β†’ 1 out8.6900 XPM109 B
ARFLbJc1…e393PV1Y
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.

1.565 Γ— 10⁹⁡(96-digit number)
15659476107409692328…41659136467347560799
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
1.565 Γ— 10⁹⁡(96-digit number)
15659476107409692328…41659136467347560799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.131 Γ— 10⁹⁡(96-digit number)
31318952214819384656…83318272934695121599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.263 Γ— 10⁹⁡(96-digit number)
62637904429638769312…66636545869390243199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.252 Γ— 10⁹⁢(97-digit number)
12527580885927753862…33273091738780486399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.505 Γ— 10⁹⁢(97-digit number)
25055161771855507725…66546183477560972799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.011 Γ— 10⁹⁢(97-digit number)
50110323543711015450…33092366955121945599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.002 Γ— 10⁹⁷(98-digit number)
10022064708742203090…66184733910243891199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.004 Γ— 10⁹⁷(98-digit number)
20044129417484406180…32369467820487782399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.008 Γ— 10⁹⁷(98-digit number)
40088258834968812360…64738935640975564799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.017 Γ— 10⁹⁷(98-digit number)
80176517669937624720…29477871281951129599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.603 Γ— 10⁹⁸(99-digit number)
16035303533987524944…58955742563902259199
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Cunningham Chain of the First 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,995,000 XPMΒ·at block #6,843,827 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