XPM Prime Explorer symbol
XPMPrime Explorer

Block #172,483

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/20/2013, 7:10:59 AM Β· Difficulty 9.8618 Β· 6,636,174 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4dc8042658b178fed1c94308106693191be4192687077f82c21d637981476560
View on Chainz β†—

Height

#172,483

Difficulty

9.861802

Transactions

1

Size

198 B

Version

2

Bits

09dc9f06

Nonce

414,290

Timestamp

9/20/2013, 7:10:59 AM

Confirmations

6,636,174

Mined by

⛏️ P2SHAPsobReAkcx5SDR5yCNgdMLw1ApYv3Lvms

Merkle Root

da1a12aff37ee5840269faf87434f89781050360fb370fdb4d8d57f58bee7a9e
Transactions (1)
Coinbaseda1a12aff37ee5…8d57f58bee7a9e
1 in β†’ 1 out10.2700 XPM109 B
APsobReA…pYv3Lvms
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.

3.918 Γ— 10⁹²(93-digit number)
39187843328300204072…84798054934245495039
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
3.918 Γ— 10⁹²(93-digit number)
39187843328300204072…84798054934245495039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.837 Γ— 10⁹²(93-digit number)
78375686656600408144…69596109868490990079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.567 Γ— 10⁹³(94-digit number)
15675137331320081628…39192219736981980159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.135 Γ— 10⁹³(94-digit number)
31350274662640163257…78384439473963960319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.270 Γ— 10⁹³(94-digit number)
62700549325280326515…56768878947927920639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.254 Γ— 10⁹⁴(95-digit number)
12540109865056065303…13537757895855841279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.508 Γ— 10⁹⁴(95-digit number)
25080219730112130606…27075515791711682559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.016 Γ— 10⁹⁴(95-digit number)
50160439460224261212…54151031583423365119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.003 Γ— 10⁹⁡(96-digit number)
10032087892044852242…08302063166846730239
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,713,299 XPMΒ·at block #6,808,656 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