XPM Prime Explorer symbol
XPMPrime Explorer

Block #161,270

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/12/2013, 1:33:58 PM Β· Difficulty 9.8590 Β· 6,648,781 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
663fcd8cf56771a9f0a24045277a3e379f500f99002e842b8ec8cdd73438d396
View on Chainz β†—

Height

#161,270

Difficulty

9.859005

Transactions

1

Size

197 B

Version

2

Bits

09dbe7c0

Nonce

138,248

Timestamp

9/12/2013, 1:33:58 PM

Confirmations

6,648,781

Mined by

⛏️ P2SHAWbm4AWfhyZEMkdPYLMs4FyYdBzNGrUw91

Merkle Root

8d19f0dd3dfa6935ef83648b719d99e15b00915989375bb5a6fb7924fb1b5944
Transactions (1)
Coinbase8d19f0dd3dfa69…fb7924fb1b5944
1 in β†’ 1 out10.2700 XPM109 B
AWbm4AWf…zNGrUw91
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.

1.086 Γ— 10⁹⁰(91-digit number)
10868607944684521406…62942075809201164641
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
1.086 Γ— 10⁹⁰(91-digit number)
10868607944684521406…62942075809201164641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.173 Γ— 10⁹⁰(91-digit number)
21737215889369042813…25884151618402329281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.347 Γ— 10⁹⁰(91-digit number)
43474431778738085627…51768303236804658561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.694 Γ— 10⁹⁰(91-digit number)
86948863557476171254…03536606473609317121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.738 Γ— 10⁹¹(92-digit number)
17389772711495234250…07073212947218634241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.477 Γ— 10⁹¹(92-digit number)
34779545422990468501…14146425894437268481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.955 Γ— 10⁹¹(92-digit number)
69559090845980937003…28292851788874536961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.391 Γ— 10⁹²(93-digit number)
13911818169196187400…56585703577749073921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.782 Γ— 10⁹²(93-digit number)
27823636338392374801…13171407155498147841
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:57,724,481 XPMΒ·at block #6,810,050 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.
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