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Block #163,016

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/13/2013, 5:08:42 PM Β· Difficulty 9.8616 Β· 6,663,355 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3097c7588491825fa4554a0fd8853c1fc9f467997109bff382b2d44c02fa050b
View on Chainz β†—

Height

#163,016

Difficulty

9.861594

Transactions

1

Size

199 B

Version

2

Bits

09dc9168

Nonce

38,378

Timestamp

9/13/2013, 5:08:42 PM

Confirmations

6,663,355

Mined by

⛏️ P2SHAYkoKAQ4RDKGS7byjZXQArv3A5uuj8DeZs

Merkle Root

85a65d0a59ddcbfff74887f7e011f84e0b8fcb666ef7c2e8e384bd1473acd1a7
Transactions (1)
Coinbase85a65d0a59ddcb…84bd1473acd1a7
1 in β†’ 1 out10.2700 XPM109 B
AYkoKAQ4…uuj8DeZs
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.

1.588 Γ— 10⁹⁴(95-digit number)
15887508156884489184…23753713631845504799
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
1.588 Γ— 10⁹⁴(95-digit number)
15887508156884489184…23753713631845504799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.177 Γ— 10⁹⁴(95-digit number)
31775016313768978369…47507427263691009599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.355 Γ— 10⁹⁴(95-digit number)
63550032627537956738…95014854527382019199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.271 Γ— 10⁹⁡(96-digit number)
12710006525507591347…90029709054764038399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.542 Γ— 10⁹⁡(96-digit number)
25420013051015182695…80059418109528076799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.084 Γ— 10⁹⁡(96-digit number)
50840026102030365390…60118836219056153599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.016 Γ— 10⁹⁢(97-digit number)
10168005220406073078…20237672438112307199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.033 Γ— 10⁹⁢(97-digit number)
20336010440812146156…40475344876224614399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.067 Γ— 10⁹⁢(97-digit number)
40672020881624292312…80950689752449228799
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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