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Block #64,525

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/19/2013, 7:53:31 AM Β· Difficulty 8.9819 Β· 6,745,104 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
5781a580ed1fdd7aa0689c054f0fe313f586d253f9e4601ff0fba29125a44d01
View on Chainz β†—

Height

#64,525

Difficulty

8.981911

Transactions

2

Size

391 B

Version

2

Bits

08fb5e8b

Nonce

673

Timestamp

7/19/2013, 7:53:31 AM

Confirmations

6,745,104

Mined by

⛏️ P2SHAUEDtuKkBn983aaCXiYFghrrSj9SkmzXZ1

Merkle Root

c831afe26268fbee2c20f08f17aee9bcb166f0cd4e549d917f7d482ec165bebf
Transactions (2)
Coinbase6f5475fa790fe3…e0f6c60e629dd2
1 in β†’ 1 out12.3900 XPM110 B
AUEDtuKk…9SkmzXZ1
790a42894e10ec…1712980ba70215
1 in β†’ 1 out140.9900 XPM193 B
AW7aqm7z…MZ7TogRx
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.

1.788 Γ— 10⁹⁰(91-digit number)
17886718263846035955…91222500473835555019
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
1.788 Γ— 10⁹⁰(91-digit number)
17886718263846035955…91222500473835555019
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.577 Γ— 10⁹⁰(91-digit number)
35773436527692071910…82445000947671110039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.154 Γ— 10⁹⁰(91-digit number)
71546873055384143821…64890001895342220079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.430 Γ— 10⁹¹(92-digit number)
14309374611076828764…29780003790684440159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.861 Γ— 10⁹¹(92-digit number)
28618749222153657528…59560007581368880319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.723 Γ— 10⁹¹(92-digit number)
57237498444307315056…19120015162737760639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.144 Γ— 10⁹²(93-digit number)
11447499688861463011…38240030325475521279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.289 Γ— 10⁹²(93-digit number)
22894999377722926022…76480060650951042559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.578 Γ— 10⁹²(93-digit number)
45789998755445852045…52960121301902085119
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,721,110 XPMΒ·at block #6,809,628 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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