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Block #1,586,469

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/16/2016, 2:12:02 AM Β· Difficulty 10.6500 Β· 5,223,770 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
96b8b3a35cf2ae43e3e1e3282f4a8675c580d4a3c41d987b90d29090898c0925
View on Chainz β†—

Height

#1,586,469

Difficulty

10.649998

Transactions

1

Size

200 B

Version

2

Bits

0aa66649

Nonce

443,418

Timestamp

5/16/2016, 2:12:02 AM

Confirmations

5,223,770

Mined by

⛏️ P2SHAXbpyooSXrgsDVAsu6AkhX5vgBbup7bQTH

Merkle Root

af67f271dd984f26b1936c60416cad94c465e434670a4b0ecda4d5c33aeb510f
Transactions (1)
Coinbaseaf67f271dd984f…a4d5c33aeb510f
1 in β†’ 1 out8.8000 XPM109 B
AXbpyooS…bup7bQTH
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.

2.067 Γ— 10⁹⁢(97-digit number)
20678258798374341046…25763980132276076419
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
2.067 Γ— 10⁹⁢(97-digit number)
20678258798374341046…25763980132276076419
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.135 Γ— 10⁹⁢(97-digit number)
41356517596748682092…51527960264552152839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.271 Γ— 10⁹⁢(97-digit number)
82713035193497364184…03055920529104305679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.654 Γ— 10⁹⁷(98-digit number)
16542607038699472836…06111841058208611359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.308 Γ— 10⁹⁷(98-digit number)
33085214077398945673…12223682116417222719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.617 Γ— 10⁹⁷(98-digit number)
66170428154797891347…24447364232834445439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.323 Γ— 10⁹⁸(99-digit number)
13234085630959578269…48894728465668890879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.646 Γ— 10⁹⁸(99-digit number)
26468171261919156539…97789456931337781759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.293 Γ— 10⁹⁸(99-digit number)
52936342523838313078…95578913862675563519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.058 Γ— 10⁹⁹(100-digit number)
10587268504767662615…91157827725351127039
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:57,725,990 XPMΒ·at block #6,810,238 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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