XPM Prime Explorer symbol
XPMPrime Explorer

Block #1,187,182

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/8/2015, 8:20:02 PM Β· Difficulty 10.8793 Β· 5,639,707 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
65e4bfde458c1638b79fd4492deee9ceff7220f7c03a5bf8ecbfe635b5dcf82e
View on Chainz β†—

Height

#1,187,182

Difficulty

10.879262

Transactions

1

Size

206 B

Version

2

Bits

0ae11757

Nonce

261,825,150

Timestamp

8/8/2015, 8:20:02 PM

Confirmations

5,639,707

Mined by

⛏️ P2SHAJCEY9yyy2DERzsA24UUtHTMGPtg97E6zm

Merkle Root

de06d520a9e0b14bc2705902be8769e96a7688c117157da0976885a922ed97f9
Transactions (1)
Coinbasede06d520a9e0b1…6885a922ed97f9
1 in β†’ 1 out8.4400 XPM116 B
AJCEY9yy…tg97E6zm
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.

5.673 Γ— 10⁹⁡(96-digit number)
56732296642760632585…53682444133815235999
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
5.673 Γ— 10⁹⁡(96-digit number)
56732296642760632585…53682444133815235999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.134 Γ— 10⁹⁢(97-digit number)
11346459328552126517…07364888267630471999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.269 Γ— 10⁹⁢(97-digit number)
22692918657104253034…14729776535260943999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.538 Γ— 10⁹⁢(97-digit number)
45385837314208506068…29459553070521887999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.077 Γ— 10⁹⁢(97-digit number)
90771674628417012136…58919106141043775999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.815 Γ— 10⁹⁷(98-digit number)
18154334925683402427…17838212282087551999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.630 Γ— 10⁹⁷(98-digit number)
36308669851366804854…35676424564175103999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.261 Γ— 10⁹⁷(98-digit number)
72617339702733609709…71352849128350207999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.452 Γ— 10⁹⁸(99-digit number)
14523467940546721941…42705698256700415999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.904 Γ— 10⁹⁸(99-digit number)
29046935881093443883…85411396513400831999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
5.809 Γ— 10⁹⁸(99-digit number)
58093871762186887767…70822793026801663999
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,859,277 XPMΒ·at block #6,826,888 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