XPM Prime Explorer symbol
XPMPrime Explorer

Block #180,690

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/26/2013, 12:05:00 AM Β· Difficulty 9.8620 Β· 6,628,800 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1ee517d1e3c3cb1bdd421401de3c8d73984e70c718eccea132cf58bceb9d0fa8
View on Chainz β†—

Height

#180,690

Difficulty

9.861994

Transactions

2

Size

426 B

Version

2

Bits

09dcaba3

Nonce

20,095

Timestamp

9/26/2013, 12:05:00 AM

Confirmations

6,628,800

Mined by

⛏️ P2SHAdhG927tpvDa8VHS6PpAxUyR8Yodsr5WMT

Merkle Root

b7d60b8c201d4a66208e28a30b169b0965cbd9ddf7749cd873bbce744abebc0a
Transactions (2)
Coinbase26fab5d524fa67…575787b0eb4a31
1 in β†’ 1 out10.2800 XPM109 B
AdhG927t…odsr5WMT
61b5424e599762…65e761c0124cad
1 in β†’ 2 out3.1780 XPM226 B
AYDnRpDp…134o36uaAQFBW6Ev…RQ4H4EFe
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.

2.410 Γ— 10⁹⁷(98-digit number)
24103951893099754934…78410444271630899199
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
2.410 Γ— 10⁹⁷(98-digit number)
24103951893099754934…78410444271630899199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.820 Γ— 10⁹⁷(98-digit number)
48207903786199509868…56820888543261798399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.641 Γ— 10⁹⁷(98-digit number)
96415807572399019737…13641777086523596799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.928 Γ— 10⁹⁸(99-digit number)
19283161514479803947…27283554173047193599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.856 Γ— 10⁹⁸(99-digit number)
38566323028959607895…54567108346094387199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.713 Γ— 10⁹⁸(99-digit number)
77132646057919215790…09134216692188774399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.542 Γ— 10⁹⁹(100-digit number)
15426529211583843158…18268433384377548799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.085 Γ— 10⁹⁹(100-digit number)
30853058423167686316…36536866768755097599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.170 Γ— 10⁹⁹(100-digit number)
61706116846335372632…73073733537510195199
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:57,719,992 XPMΒ·at block #6,809,489 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