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Block #90,307

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/31/2013, 12:44:58 AM Β· Difficulty 9.2473 Β· 6,734,251 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
356e92b35a5d3c14664a043fbae1cf37cb006d57e1ef2180b15b2d83ad53c332
View on Chainz β†—

Height

#90,307

Difficulty

9.247338

Transactions

1

Size

200 B

Version

2

Bits

093f5189

Nonce

221,913

Timestamp

7/31/2013, 12:44:58 AM

Confirmations

6,734,251

Mined by

⛏️ P2SHAeEXQxqG1a9HUoHobjrNQ1M2oHJ2q5dxWc

Merkle Root

d97f134db8d41236313b06e0ae46bd008aa132b4c3708c2904861381b3a66a8b
Transactions (1)
Coinbased97f134db8d412…861381b3a66a8b
1 in β†’ 1 out11.6800 XPM109 B
AeEXQxqG…J2q5dxWc
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.

1.121 Γ— 10⁹⁢(97-digit number)
11215542399533501184…17188663142630998279
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
1.121 Γ— 10⁹⁢(97-digit number)
11215542399533501184…17188663142630998279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.243 Γ— 10⁹⁢(97-digit number)
22431084799067002368…34377326285261996559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.486 Γ— 10⁹⁢(97-digit number)
44862169598134004737…68754652570523993119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.972 Γ— 10⁹⁢(97-digit number)
89724339196268009475…37509305141047986239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.794 Γ— 10⁹⁷(98-digit number)
17944867839253601895…75018610282095972479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.588 Γ— 10⁹⁷(98-digit number)
35889735678507203790…50037220564191944959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.177 Γ— 10⁹⁷(98-digit number)
71779471357014407580…00074441128383889919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.435 Γ— 10⁹⁸(99-digit number)
14355894271402881516…00148882256767779839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.871 Γ— 10⁹⁸(99-digit number)
28711788542805763032…00297764513535559679
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
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