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Block #494,084

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/16/2014, 12:16:36 AM Β· Difficulty 10.7124 Β· 6,309,594 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
5c8ca76481cab225655d5aafa744d573bb94fa9a4db8e73ec4dd81a0f4435d82
View on Chainz β†—

Height

#494,084

Difficulty

10.712375

Transactions

2

Size

1.29 KB

Version

2

Bits

0ab65e2e

Nonce

548,027

Timestamp

4/16/2014, 12:16:36 AM

Confirmations

6,309,594

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

4f4ddfb8d21e8c483b5ec2db7bdfa59c62bb56c7ad9f37a7336a01887f9e5bcc
Transactions (2)
Coinbasefab51f32c027a8…6678822f073d82
1 in β†’ 1 out8.7200 XPM110 B
AeKNrjNj…1NEq95Ta
6dd4c6618bbca7…57b9c89bcb0437
7 in β†’ 2 out21.3179 XPM1.09 KB
AQm4yuyC…5LjdLYx7AKm7aWWW…bV7nhyYS
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.

1.427 Γ— 10⁹⁷(98-digit number)
14275053220619553090…67866315550998920959
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
1.427 Γ— 10⁹⁷(98-digit number)
14275053220619553090…67866315550998920959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.855 Γ— 10⁹⁷(98-digit number)
28550106441239106181…35732631101997841919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.710 Γ— 10⁹⁷(98-digit number)
57100212882478212362…71465262203995683839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.142 Γ— 10⁹⁸(99-digit number)
11420042576495642472…42930524407991367679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.284 Γ— 10⁹⁸(99-digit number)
22840085152991284945…85861048815982735359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.568 Γ— 10⁹⁸(99-digit number)
45680170305982569890…71722097631965470719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.136 Γ— 10⁹⁸(99-digit number)
91360340611965139780…43444195263930941439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.827 Γ— 10⁹⁹(100-digit number)
18272068122393027956…86888390527861882879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.654 Γ— 10⁹⁹(100-digit number)
36544136244786055912…73776781055723765759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.308 Γ— 10⁹⁹(100-digit number)
73088272489572111824…47553562111447531519
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:57,673,459 XPMΒ·at block #6,803,677 Β· updates every 60s
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