XPM Prime Explorer symbol
XPMPrime Explorer

Block #159,112

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/10/2013, 9:20:26 PM Β· Difficulty 9.8659 Β· 6,647,589 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
5f129f8116d2c72c783bb329be58971866e6c4c0cab56ba59f534e4be86e25c7
View on Chainz β†—

Height

#159,112

Difficulty

9.865921

Transactions

1

Size

197 B

Version

2

Bits

09ddacfe

Nonce

137,589

Timestamp

9/10/2013, 9:20:26 PM

Confirmations

6,647,589

Mined by

⛏️ P2SHAPbne1gSsQ4A6bqfDhiLcmWiENFS5g2nZv

Merkle Root

12613262d96dae98e7d76cb4a75e1b14e4eef086d820e47798c6bad65f1cd82a
Transactions (1)
Coinbase12613262d96dae…c6bad65f1cd82a
1 in β†’ 1 out10.2600 XPM109 B
APbne1gS…FS5g2nZv
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.

1.213 Γ— 10⁹¹(92-digit number)
12131727428833916045…15264256961389651199
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
1.213 Γ— 10⁹¹(92-digit number)
12131727428833916045…15264256961389651199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.426 Γ— 10⁹¹(92-digit number)
24263454857667832090…30528513922779302399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.852 Γ— 10⁹¹(92-digit number)
48526909715335664180…61057027845558604799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.705 Γ— 10⁹¹(92-digit number)
97053819430671328361…22114055691117209599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.941 Γ— 10⁹²(93-digit number)
19410763886134265672…44228111382234419199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.882 Γ— 10⁹²(93-digit number)
38821527772268531344…88456222764468838399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.764 Γ— 10⁹²(93-digit number)
77643055544537062689…76912445528937676799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.552 Γ— 10⁹³(94-digit number)
15528611108907412537…53824891057875353599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.105 Γ— 10⁹³(94-digit number)
31057222217814825075…07649782115750707199
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:57,697,705 XPMΒ·at block #6,806,700 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