XPM Prime Explorer symbol
XPMPrime Explorer

Block #340,024

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/2/2014, 12:29:50 PM Β· Difficulty 10.1280 Β· 6,487,209 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
25e9e835c328adf31331569c0e6382aa3e2bf72457b290ccf0eb8bf76b19cc70
View on Chainz β†—

Height

#340,024

Difficulty

10.128028

Transactions

2

Size

540 B

Version

2

Bits

0a20c671

Nonce

259,397

Timestamp

1/2/2014, 12:29:50 PM

Confirmations

6,487,209

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

2e438280c38c7e975885bf0c038a9428e24d9df0e4815dced94f32fbcb938f50
Transactions (2)
Coinbasec792e50c21ead0…8276c9c0d79454
1 in β†’ 1 out9.7470 XPM110 B
AeKNrjNj…1NEq95Ta
9fdace3d264b64…aad3e94b1ca5a4
2 in β†’ 1 out3.9900 XPM340 B
ARZVEKfH…S8hZNgTK
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.

4.467 Γ— 10⁹⁡(96-digit number)
44675925788202681689…47283221399795700839
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
4.467 Γ— 10⁹⁡(96-digit number)
44675925788202681689…47283221399795700839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.935 Γ— 10⁹⁡(96-digit number)
89351851576405363379…94566442799591401679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.787 Γ— 10⁹⁢(97-digit number)
17870370315281072675…89132885599182803359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.574 Γ— 10⁹⁢(97-digit number)
35740740630562145351…78265771198365606719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.148 Γ— 10⁹⁢(97-digit number)
71481481261124290703…56531542396731213439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.429 Γ— 10⁹⁷(98-digit number)
14296296252224858140…13063084793462426879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.859 Γ— 10⁹⁷(98-digit number)
28592592504449716281…26126169586924853759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.718 Γ— 10⁹⁷(98-digit number)
57185185008899432562…52252339173849707519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.143 Γ— 10⁹⁸(99-digit number)
11437037001779886512…04504678347699415039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.287 Γ— 10⁹⁸(99-digit number)
22874074003559773025…09009356695398830079
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:57,861,964 XPMΒ·at block #6,827,232 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