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Block #93,768

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/2/2013, 3:56:47 PM Β· Difficulty 9.1967 Β· 6,722,578 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d3ad4bcc0d87237432022714029b41793b460368f58805be8bff8287bbe54758
View on Chainz β†—

Height

#93,768

Difficulty

9.196694

Transactions

1

Size

199 B

Version

2

Bits

09325a88

Nonce

416,956

Timestamp

8/2/2013, 3:56:47 PM

Confirmations

6,722,578

Mined by

⛏️ P2SHAXvMMum1Pa5kWMWJFC5uKC4CTEy1ajpFRb

Merkle Root

3680b447591aa9df5f506acf55e793ed1c4b96095d48ef725b991af45c1aa7ac
Transactions (1)
Coinbase3680b447591aa9…991af45c1aa7ac
1 in β†’ 1 out11.8100 XPM109 B
AXvMMum1…y1ajpFRb
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.

6.837 Γ— 10⁹³(94-digit number)
68372644963341921566…50429969680836316659
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
6.837 Γ— 10⁹³(94-digit number)
68372644963341921566…50429969680836316659
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.367 Γ— 10⁹⁴(95-digit number)
13674528992668384313…00859939361672633319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.734 Γ— 10⁹⁴(95-digit number)
27349057985336768626…01719878723345266639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.469 Γ— 10⁹⁴(95-digit number)
54698115970673537253…03439757446690533279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.093 Γ— 10⁹⁡(96-digit number)
10939623194134707450…06879514893381066559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.187 Γ— 10⁹⁡(96-digit number)
21879246388269414901…13759029786762133119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.375 Γ— 10⁹⁡(96-digit number)
43758492776538829802…27518059573524266239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.751 Γ— 10⁹⁡(96-digit number)
87516985553077659604…55036119147048532479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.750 Γ— 10⁹⁢(97-digit number)
17503397110615531920…10072238294097064959
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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