XPM Prime Explorer symbol
XPMPrime Explorer

Block #177,490

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/23/2013, 5:09:15 PM Β· Difficulty 9.8644 Β· 6,636,985 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d329295cfe2ac88b7ffa99f2b7b36a990723038947d7ef4e15120bbf05273535
View on Chainz β†—

Height

#177,490

Difficulty

9.864440

Transactions

1

Size

200 B

Version

2

Bits

09dd4bf8

Nonce

46,255

Timestamp

9/23/2013, 5:09:15 PM

Confirmations

6,636,985

Mined by

⛏️ P2SHASiN1vnGnb4VLXNU9Yym429CfsnPBYx4TC

Merkle Root

fd01add236598ff3d1b25989d53ca52f740b50eea10fadd078fcbbbbc54aa30a
Transactions (1)
Coinbasefd01add236598f…fcbbbbc54aa30a
1 in β†’ 1 out10.2600 XPM109 B
ASiN1vnG…nPBYx4TC
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.

2.517 Γ— 10⁹⁢(97-digit number)
25177657130894442840…00340374087882333439
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
2.517 Γ— 10⁹⁢(97-digit number)
25177657130894442840…00340374087882333439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.035 Γ— 10⁹⁢(97-digit number)
50355314261788885681…00680748175764666879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.007 Γ— 10⁹⁷(98-digit number)
10071062852357777136…01361496351529333759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.014 Γ— 10⁹⁷(98-digit number)
20142125704715554272…02722992703058667519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.028 Γ— 10⁹⁷(98-digit number)
40284251409431108545…05445985406117335039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.056 Γ— 10⁹⁷(98-digit number)
80568502818862217090…10891970812234670079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.611 Γ— 10⁹⁸(99-digit number)
16113700563772443418…21783941624469340159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.222 Γ— 10⁹⁸(99-digit number)
32227401127544886836…43567883248938680319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.445 Γ— 10⁹⁸(99-digit number)
64454802255089773672…87135766497877360639
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:57,759,875 XPMΒ·at block #6,814,474 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