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Block #164,940

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/14/2013, 11:24:56 PM Β· Difficulty 9.8646 Β· 6,659,952 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
224c36e6d73cbd9e09cc886bf8421d625df1806bfba94f77dd0a5af8b38a0f8d
View on Chainz β†—

Height

#164,940

Difficulty

9.864576

Transactions

1

Size

198 B

Version

2

Bits

09dd54db

Nonce

12,676

Timestamp

9/14/2013, 11:24:56 PM

Confirmations

6,659,952

Mined by

⛏️ P2SHAVJaZtXCr3NXSK79aMri9GXJU2gGZDZ3Yk

Merkle Root

2c907c14874977c14f72cd78fcb5006ce7535feb10cc095608ff6b4c3bde6788
Transactions (1)
Coinbase2c907c14874977…ff6b4c3bde6788
1 in β†’ 1 out10.2600 XPM109 B
AVJaZtXC…gGZDZ3Yk
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.

1.338 Γ— 10⁹³(94-digit number)
13389516949632488884…70413202550290541839
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
1.338 Γ— 10⁹³(94-digit number)
13389516949632488884…70413202550290541839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.677 Γ— 10⁹³(94-digit number)
26779033899264977769…40826405100581083679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.355 Γ— 10⁹³(94-digit number)
53558067798529955539…81652810201162167359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.071 Γ— 10⁹⁴(95-digit number)
10711613559705991107…63305620402324334719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.142 Γ— 10⁹⁴(95-digit number)
21423227119411982215…26611240804648669439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.284 Γ— 10⁹⁴(95-digit number)
42846454238823964431…53222481609297338879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.569 Γ— 10⁹⁴(95-digit number)
85692908477647928863…06444963218594677759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.713 Γ— 10⁹⁡(96-digit number)
17138581695529585772…12889926437189355519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.427 Γ— 10⁹⁡(96-digit number)
34277163391059171545…25779852874378711039
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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