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Block #183,824

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/28/2013, 6:42:42 AM Β· Difficulty 9.8584 Β· 6,630,273 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
123083dd4a6148bfde66f5032b03eaaea5158e5fd346cd294d919c6f84004ad8
View on Chainz β†—

Height

#183,824

Difficulty

9.858415

Transactions

1

Size

199 B

Version

2

Bits

09dbc110

Nonce

12,661

Timestamp

9/28/2013, 6:42:42 AM

Confirmations

6,630,273

Mined by

⛏️ P2SHAWbQMT1UFX9Fb1nejhFo5DMbcK8Pt4ow7J

Merkle Root

a6bac8c04dd4b9dd34e5f516ba8eaaece65bbb6ac3f6612f371c76067ece7262
Transactions (1)
Coinbasea6bac8c04dd4b9…1c76067ece7262
1 in β†’ 1 out10.2700 XPM109 B
AWbQMT1U…8Pt4ow7J
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.

3.479 Γ— 10⁹⁴(95-digit number)
34796830866285675604…69389693054945249439
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
3.479 Γ— 10⁹⁴(95-digit number)
34796830866285675604…69389693054945249439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.959 Γ— 10⁹⁴(95-digit number)
69593661732571351208…38779386109890498879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.391 Γ— 10⁹⁡(96-digit number)
13918732346514270241…77558772219780997759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.783 Γ— 10⁹⁡(96-digit number)
27837464693028540483…55117544439561995519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.567 Γ— 10⁹⁡(96-digit number)
55674929386057080966…10235088879123991039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.113 Γ— 10⁹⁢(97-digit number)
11134985877211416193…20470177758247982079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.226 Γ— 10⁹⁢(97-digit number)
22269971754422832386…40940355516495964159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.453 Γ— 10⁹⁢(97-digit number)
44539943508845664773…81880711032991928319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.907 Γ— 10⁹⁢(97-digit number)
89079887017691329546…63761422065983856639
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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