XPM Prime Explorer symbol
XPMPrime Explorer

Block #839,216

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/4/2014, 6:04:48 AM Β· Difficulty 10.9747 Β· 5,971,710 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
49ff66f306ce36148d5160f28b9b5dbb57570f207ed9e404d289333a7c562f74
View on Chainz β†—

Height

#839,216

Difficulty

10.974686

Transactions

2

Size

6.35 KB

Version

2

Bits

0af98508

Nonce

74,630,774

Timestamp

12/4/2014, 6:04:48 AM

Confirmations

5,971,710

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

7cfa7380f71c45ea793deffa8f5413431ab4b88a7a602d77c1988b6f215fb1eb
Transactions (2)
Coinbase4ac76761506e61…9f0bb4c9dee6e3
1 in β†’ 1 out8.3700 XPM116 B
ANSXnLY2…Sd25TjkD
a7dcecb1afa514…0e86dd40871cad
42 in β†’ 2 out500.0100 XPM6.15 KB
AJjnK9uC…VreFquR4AX9TW6oz…GjwVr7FF
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.

1.907 Γ— 10⁹⁷(98-digit number)
19071948521584416230…59760325539258499999
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
1.907 Γ— 10⁹⁷(98-digit number)
19071948521584416230…59760325539258499999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.814 Γ— 10⁹⁷(98-digit number)
38143897043168832460…19520651078516999999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.628 Γ— 10⁹⁷(98-digit number)
76287794086337664920…39041302157033999999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.525 Γ— 10⁹⁸(99-digit number)
15257558817267532984…78082604314067999999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.051 Γ— 10⁹⁸(99-digit number)
30515117634535065968…56165208628135999999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.103 Γ— 10⁹⁸(99-digit number)
61030235269070131936…12330417256271999999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.220 Γ— 10⁹⁹(100-digit number)
12206047053814026387…24660834512543999999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.441 Γ— 10⁹⁹(100-digit number)
24412094107628052774…49321669025087999999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.882 Γ— 10⁹⁹(100-digit number)
48824188215256105548…98643338050175999999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
9.764 Γ— 10⁹⁹(100-digit number)
97648376430512211097…97286676100351999999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.952 Γ— 10¹⁰⁰(101-digit number)
19529675286102442219…94573352200703999999
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:57,731,510 XPMΒ·at block #6,810,925 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