XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,223,135

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/26/2017, 3:48:55 AM Β· Difficulty 10.9459 Β· 4,618,195 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7c8e75bd7ef732f550e42284a2ea4cc74df916a80468f65074f4a803fd297f6e
View on Chainz β†—

Height

#2,223,135

Difficulty

10.945861

Transactions

1

Size

200 B

Version

2

Bits

0af223ef

Nonce

567,298,993

Timestamp

7/26/2017, 3:48:55 AM

Confirmations

4,618,195

Mined by

⛏️ P2SHARzpxgGMCB8TERBy9oRCufd5vNqrQnqYY4

Merkle Root

f2446c4ac73a8c33fcccc72d18e28c88c775a604041e18292359e074f71e5b15
Transactions (1)
Coinbasef2446c4ac73a8c…59e074f71e5b15
1 in β†’ 1 out8.3300 XPM110 B
ARzpxgGM…qrQnqYY4
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.

2.381 Γ— 10⁹⁡(96-digit number)
23815240073763477403…61110777925801223681
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
2.381 Γ— 10⁹⁡(96-digit number)
23815240073763477403…61110777925801223681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.763 Γ— 10⁹⁡(96-digit number)
47630480147526954806…22221555851602447361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.526 Γ— 10⁹⁡(96-digit number)
95260960295053909613…44443111703204894721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.905 Γ— 10⁹⁢(97-digit number)
19052192059010781922…88886223406409789441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.810 Γ— 10⁹⁢(97-digit number)
38104384118021563845…77772446812819578881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.620 Γ— 10⁹⁢(97-digit number)
76208768236043127690…55544893625639157761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.524 Γ— 10⁹⁷(98-digit number)
15241753647208625538…11089787251278315521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.048 Γ— 10⁹⁷(98-digit number)
30483507294417251076…22179574502556631041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.096 Γ— 10⁹⁷(98-digit number)
60967014588834502152…44359149005113262081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.219 Γ— 10⁹⁸(99-digit number)
12193402917766900430…88718298010226524161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.438 Γ— 10⁹⁸(99-digit number)
24386805835533800861…77436596020453048321
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:57,975,003 XPMΒ·at block #6,841,329 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