XPM Prime Explorer symbol
XPMPrime Explorer

Block #154,218

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/7/2013, 12:43:46 PM Β· Difficulty 9.8642 Β· 6,660,681 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
472e279cc892a0163192f7196f6d3c6094b77c0f2b3df58cd22d50b47267377e
View on Chainz β†—

Height

#154,218

Difficulty

9.864179

Transactions

1

Size

199 B

Version

2

Bits

09dd3ada

Nonce

191,427

Timestamp

9/7/2013, 12:43:46 PM

Confirmations

6,660,681

Mined by

⛏️ P2SHATr36r6GPrDWuY8aErt6RmRFsBKgmGvw5f

Merkle Root

9bfc5cb7a70f329f0cebbf959be256dbb0501c28122bd1ba2a792ee3d7367973
Transactions (1)
Coinbase9bfc5cb7a70f32…792ee3d7367973
1 in β†’ 1 out10.2600 XPM109 B
ATr36r6G…KgmGvw5f
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.

3.204 Γ— 10⁹⁡(96-digit number)
32047784496294590660…65143509141707614561
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
3.204 Γ— 10⁹⁡(96-digit number)
32047784496294590660…65143509141707614561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.409 Γ— 10⁹⁡(96-digit number)
64095568992589181321…30287018283415229121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.281 Γ— 10⁹⁢(97-digit number)
12819113798517836264…60574036566830458241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.563 Γ— 10⁹⁢(97-digit number)
25638227597035672528…21148073133660916481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.127 Γ— 10⁹⁢(97-digit number)
51276455194071345057…42296146267321832961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.025 Γ— 10⁹⁷(98-digit number)
10255291038814269011…84592292534643665921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.051 Γ— 10⁹⁷(98-digit number)
20510582077628538022…69184585069287331841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.102 Γ— 10⁹⁷(98-digit number)
41021164155257076045…38369170138574663681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.204 Γ— 10⁹⁷(98-digit number)
82042328310514152091…76738340277149327361
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,763,281 XPMΒ·at block #6,814,898 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