XPM Prime Explorer symbol
XPMPrime Explorer

Block #162,026

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/13/2013, 1:09:17 AM Β· Difficulty 9.8607 Β· 6,648,489 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
bc59189de23c5594b54421193e951441b18905eb4963a2213571400355924db6
View on Chainz β†—

Height

#162,026

Difficulty

9.860724

Transactions

1

Size

199 B

Version

2

Bits

09dc5861

Nonce

46,209

Timestamp

9/13/2013, 1:09:17 AM

Confirmations

6,648,489

Mined by

⛏️ P2SHAdDUNTYmz3S4v6JdhjgL2fyWhUv4Zjqa77

Merkle Root

5ffdb71dcfa6ab05da5729b6fbcfe4ba01b60853ceb6b3129888c5db58d0b312
Transactions (1)
Coinbase5ffdb71dcfa6ab…88c5db58d0b312
1 in β†’ 1 out10.2700 XPM109 B
AdDUNTYm…v4Zjqa77
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.

1.061 Γ— 10⁹⁡(96-digit number)
10616793038165360867…61901707011364819199
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
1.061 Γ— 10⁹⁡(96-digit number)
10616793038165360867…61901707011364819199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.123 Γ— 10⁹⁡(96-digit number)
21233586076330721735…23803414022729638399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.246 Γ— 10⁹⁡(96-digit number)
42467172152661443470…47606828045459276799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.493 Γ— 10⁹⁡(96-digit number)
84934344305322886940…95213656090918553599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.698 Γ— 10⁹⁢(97-digit number)
16986868861064577388…90427312181837107199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.397 Γ— 10⁹⁢(97-digit number)
33973737722129154776…80854624363674214399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.794 Γ— 10⁹⁢(97-digit number)
67947475444258309552…61709248727348428799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.358 Γ— 10⁹⁷(98-digit number)
13589495088851661910…23418497454696857599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.717 Γ— 10⁹⁷(98-digit number)
27178990177703323820…46836994909393715199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.435 Γ— 10⁹⁷(98-digit number)
54357980355406647641…93673989818787430399
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,728,205 XPMΒ·at block #6,810,514 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