XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,872,701

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/8/2018, 2:32:40 PM Β· Difficulty 11.6654 Β· 3,967,565 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
402e1dbed39be7f2c3acd6b464950d086b3fc8e244ee76e003575575d9569684
View on Chainz β†—

Height

#2,872,701

Difficulty

11.665418

Transactions

1

Size

201 B

Version

2

Bits

0baa58d3

Nonce

349,810,773

Timestamp

10/8/2018, 2:32:40 PM

Confirmations

3,967,565

Mined by

⛏️ P2SHAa7XFLtngJYBpwTFnVVNZ6ehH5jZ6aRKEo

Merkle Root

cec257240b3d69a1c1712afd4365049f2052719097d7a8ae19d22859f95ba1be
Transactions (1)
Coinbasecec257240b3d69…d22859f95ba1be
1 in β†’ 1 out7.3400 XPM110 B
Aa7XFLtn…jZ6aRKEo
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.

4.755 Γ— 10⁹⁷(98-digit number)
47556803953948365240…42753926298060206081
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
4.755 Γ— 10⁹⁷(98-digit number)
47556803953948365240…42753926298060206081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.511 Γ— 10⁹⁷(98-digit number)
95113607907896730480…85507852596120412161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.902 Γ— 10⁹⁸(99-digit number)
19022721581579346096…71015705192240824321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.804 Γ— 10⁹⁸(99-digit number)
38045443163158692192…42031410384481648641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.609 Γ— 10⁹⁸(99-digit number)
76090886326317384384…84062820768963297281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.521 Γ— 10⁹⁹(100-digit number)
15218177265263476876…68125641537926594561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.043 Γ— 10⁹⁹(100-digit number)
30436354530526953753…36251283075853189121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.087 Γ— 10⁹⁹(100-digit number)
60872709061053907507…72502566151706378241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.217 Γ— 10¹⁰⁰(101-digit number)
12174541812210781501…45005132303412756481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.434 Γ— 10¹⁰⁰(101-digit number)
24349083624421563002…90010264606825512961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.869 Γ— 10¹⁰⁰(101-digit number)
48698167248843126005…80020529213651025921
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 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
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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,966,442 XPMΒ·at block #6,840,265 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