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Block #1,394,279

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/1/2016, 8:07:17 AM Β· Difficulty 10.8129 Β· 5,421,767 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
64924fbebd3111355f498423f5d80ec20f69f743d9df314b1eeea41f29581076
View on Chainz β†—

Height

#1,394,279

Difficulty

10.812943

Transactions

2

Size

2.58 KB

Version

2

Bits

0ad01d0e

Nonce

1,227,552,081

Timestamp

1/1/2016, 8:07:17 AM

Confirmations

5,421,767

Mined by

⛏️ P2SHAaquYkJ3k7GuNjEQBMBQefiGm529aA9iz1

Merkle Root

447b29d835545c363c1376efe8b9662bdf5c4f0d9fe635577c1248f92a4e911a
Transactions (2)
Coinbasee752b4d28736cd…65630310e6384f
1 in β†’ 1 out8.5700 XPM110 B
AaquYkJ3…29aA9iz1
f16382d5315a49…0c7f8bf1f359ac
16 in β†’ 2 out4.2553 XPM2.39 KB
ASeoFGwY…REXLsSxzAHS2XGqZ…1kAeiCBq
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.

3.501 Γ— 10⁹³(94-digit number)
35015320313603677975…84329160474268574719
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
3.501 Γ— 10⁹³(94-digit number)
35015320313603677975…84329160474268574719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.003 Γ— 10⁹³(94-digit number)
70030640627207355951…68658320948537149439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.400 Γ— 10⁹⁴(95-digit number)
14006128125441471190…37316641897074298879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.801 Γ— 10⁹⁴(95-digit number)
28012256250882942380…74633283794148597759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.602 Γ— 10⁹⁴(95-digit number)
56024512501765884760…49266567588297195519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.120 Γ— 10⁹⁡(96-digit number)
11204902500353176952…98533135176594391039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.240 Γ— 10⁹⁡(96-digit number)
22409805000706353904…97066270353188782079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.481 Γ— 10⁹⁡(96-digit number)
44819610001412707808…94132540706377564159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.963 Γ— 10⁹⁡(96-digit number)
89639220002825415617…88265081412755128319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.792 Γ— 10⁹⁢(97-digit number)
17927844000565083123…76530162825510256639
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:57,772,484 XPMΒ·at block #6,816,045 Β· updates every 60s
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