XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,116,025

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/14/2017, 3:44:07 PM Β· Difficulty 10.9030 Β· 4,726,681 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
435eb955357727509f2298e80fe1f755b74bb6cdb8b519f7d81a7609ebaf7cee
View on Chainz β†—

Height

#2,116,025

Difficulty

10.903017

Transactions

1

Size

243 B

Version

2

Bits

0ae72c1f

Nonce

1,420,814,408

Timestamp

5/14/2017, 3:44:07 PM

Confirmations

4,726,681

Mined by

⛏️ P2SHAMMJ7Ku9ctFmjCbBPtKsnh34K5ZYGbYo5z

Merkle Root

369f03c4891b35c39cb57f69b069357d054631c3790383df0e10f7aef642ae08
Transactions (1)
Coinbase369f03c4891b35…10f7aef642ae08
1 in β†’ 2 out8.4000 XPM152 B
AMMJ7Ku9…ZYGbYo5zAXbk7f7A…Tx7JECPG
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.

4.999 Γ— 10⁹⁷(98-digit number)
49991791729707534179…20124109103276861441
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
4.999 Γ— 10⁹⁷(98-digit number)
49991791729707534179…20124109103276861441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.998 Γ— 10⁹⁷(98-digit number)
99983583459415068358…40248218206553722881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.999 Γ— 10⁹⁸(99-digit number)
19996716691883013671…80496436413107445761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.999 Γ— 10⁹⁸(99-digit number)
39993433383766027343…60992872826214891521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.998 Γ— 10⁹⁸(99-digit number)
79986866767532054686…21985745652429783041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.599 Γ— 10⁹⁹(100-digit number)
15997373353506410937…43971491304859566081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.199 Γ— 10⁹⁹(100-digit number)
31994746707012821874…87942982609719132161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.398 Γ— 10⁹⁹(100-digit number)
63989493414025643749…75885965219438264321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.279 Γ— 10¹⁰⁰(101-digit number)
12797898682805128749…51771930438876528641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.559 Γ— 10¹⁰⁰(101-digit number)
25595797365610257499…03543860877753057281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
5.119 Γ— 10¹⁰⁰(101-digit number)
51191594731220514999…07087721755506114561
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:57,985,998 XPMΒ·at block #6,842,705 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