XPM Prime Explorer symbol
XPMPrime Explorer

Block #419,363

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 2/25/2014, 1:10:57 PM Β· Difficulty 10.3866 Β· 6,385,900 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c9caf2bc41c432cc413b2da82baa9401c54c86e5ce666a766ae78e516f61aa6b
View on Chainz β†—

Height

#419,363

Difficulty

10.386586

Transactions

2

Size

723 B

Version

2

Bits

0a62f74a

Nonce

90,096

Timestamp

2/25/2014, 1:10:57 PM

Confirmations

6,385,900

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

c5a70eb50f455830ba1d9d5b7ca1ab9c58ca6496daeafde553ac07cc68c5cf93
Transactions (2)
Coinbase2c94d215b252a3…5bacd99061183a
1 in β†’ 1 out9.2700 XPM110 B
AeKNrjNj…1NEq95Ta
2e38325fc9362b…718360406c72f5
3 in β†’ 2 out149.9103 XPM523 B
Adg89rJ3…FC9oNoweAXmFMNGW…C6e1YBwe
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.

1.441 Γ— 10⁹⁴(95-digit number)
14411798682985991906…34104213007739851199
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
1.441 Γ— 10⁹⁴(95-digit number)
14411798682985991906…34104213007739851199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.882 Γ— 10⁹⁴(95-digit number)
28823597365971983812…68208426015479702399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.764 Γ— 10⁹⁴(95-digit number)
57647194731943967624…36416852030959404799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.152 Γ— 10⁹⁡(96-digit number)
11529438946388793524…72833704061918809599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.305 Γ— 10⁹⁡(96-digit number)
23058877892777587049…45667408123837619199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.611 Γ— 10⁹⁡(96-digit number)
46117755785555174099…91334816247675238399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.223 Γ— 10⁹⁡(96-digit number)
92235511571110348198…82669632495350476799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.844 Γ— 10⁹⁢(97-digit number)
18447102314222069639…65339264990700953599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.689 Γ— 10⁹⁢(97-digit number)
36894204628444139279…30678529981401907199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.378 Γ— 10⁹⁢(97-digit number)
73788409256888278559…61357059962803814399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.475 Γ— 10⁹⁷(98-digit number)
14757681851377655711…22714119925607628799
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:57,686,174 XPMΒ·at block #6,805,262 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