XPM Prime Explorer symbol
XPMPrime Explorer

Block #490,269

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/13/2014, 6:37:50 PM Β· Difficulty 10.6749 Β· 6,336,907 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d1b617000fe9353a8f20fbcff0a208edcf8d792d93ba12156c4c1dcce286a821
View on Chainz β†—

Height

#490,269

Difficulty

10.674947

Transactions

2

Size

393 B

Version

2

Bits

0aacc954

Nonce

6,684

Timestamp

4/13/2014, 6:37:50 PM

Confirmations

6,336,907

Mined by

⛏️ P2SHAJ4rdm1rBE4sFJv4giXnMgAgKrLu9EdT6Q

Merkle Root

3c1c2b1390e9cf5fd6fd47ec76d3d20baa9ae53e47e191da2abd93b13455e9e5
Transactions (2)
Coinbase8c61ac5f428e84…92b7f4a1b2e154
1 in β†’ 1 out8.7700 XPM110 B
AJ4rdm1r…Lu9EdT6Q
d604fe370197a0…197c23ba1760fe
1 in β†’ 1 out3.0109 XPM192 B
ALcFZpaB…J5eU521J
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.

4.707 Γ— 10⁹⁷(98-digit number)
47072852040426879430…06396532373832388919
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
4.707 Γ— 10⁹⁷(98-digit number)
47072852040426879430…06396532373832388919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
9.414 Γ— 10⁹⁷(98-digit number)
94145704080853758860…12793064747664777839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.882 Γ— 10⁹⁸(99-digit number)
18829140816170751772…25586129495329555679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.765 Γ— 10⁹⁸(99-digit number)
37658281632341503544…51172258990659111359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.531 Γ— 10⁹⁸(99-digit number)
75316563264683007088…02344517981318222719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.506 Γ— 10⁹⁹(100-digit number)
15063312652936601417…04689035962636445439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.012 Γ— 10⁹⁹(100-digit number)
30126625305873202835…09378071925272890879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.025 Γ— 10⁹⁹(100-digit number)
60253250611746405670…18756143850545781759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.205 Γ— 10¹⁰⁰(101-digit number)
12050650122349281134…37512287701091563519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.410 Γ— 10¹⁰⁰(101-digit number)
24101300244698562268…75024575402183127039
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,861,505 XPMΒ·at block #6,827,175 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