XPM Prime Explorer symbol
XPMPrime Explorer

Block #417,406

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 2/24/2014, 3:48:41 AM Β· Difficulty 10.3910 Β· 6,385,147 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d84006cc38e989aff9bf69de2e6485a88efd530d22164aad8b660a384d2728f6
View on Chainz β†—

Height

#417,406

Difficulty

10.390997

Transactions

1

Size

968 B

Version

2

Bits

0a64185c

Nonce

767,647

Timestamp

2/24/2014, 3:48:41 AM

Confirmations

6,385,147

Mined by

⛏️ ~^aSAQwRN8bEjE7sawFBq7N38V9niAV8PsTcY9

Merkle Root

e204cfa9ae5853cc7fce1d6b58fc1f6ede707373dc0ba4e11c12a00baab63ca9
Transactions (1)
Coinbasee204cfa9ae5853…12a00baab63ca9
1 in β†’ 24 out9.2500 XPM879 B
AQwRN8bE…V8PsTcY9Aac9Hjdg…P4ktypc3ANNg88pG…ppn21sTeAGKhfQo2…h7fBXLX6AZV4TwxQ…8JnQqSoH
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.

8.298 Γ— 10⁹¹(92-digit number)
82983245337818935526…20942753125399167999
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
8.298 Γ— 10⁹¹(92-digit number)
82983245337818935526…20942753125399167999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.659 Γ— 10⁹²(93-digit number)
16596649067563787105…41885506250798335999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.319 Γ— 10⁹²(93-digit number)
33193298135127574210…83771012501596671999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.638 Γ— 10⁹²(93-digit number)
66386596270255148421…67542025003193343999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.327 Γ— 10⁹³(94-digit number)
13277319254051029684…35084050006386687999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.655 Γ— 10⁹³(94-digit number)
26554638508102059368…70168100012773375999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.310 Γ— 10⁹³(94-digit number)
53109277016204118737…40336200025546751999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.062 Γ— 10⁹⁴(95-digit number)
10621855403240823747…80672400051093503999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.124 Γ— 10⁹⁴(95-digit number)
21243710806481647494…61344800102187007999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.248 Γ— 10⁹⁴(95-digit number)
42487421612963294989…22689600204374015999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
8.497 Γ— 10⁹⁴(95-digit number)
84974843225926589979…45379200408748031999
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:57,664,437 XPMΒ·at block #6,802,552 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