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Block #181,783

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/26/2013, 7:32:29 PM Β· Difficulty 9.8602 Β· 6,628,506 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
1d0083559a0ca74bb847df3b5dfedab5d2e08d50d591d55193396f515e56e170
View on Chainz β†—

Height

#181,783

Difficulty

9.860181

Transactions

1

Size

199 B

Version

2

Bits

09dc34cb

Nonce

17,460

Timestamp

9/26/2013, 7:32:29 PM

Confirmations

6,628,506

Mined by

⛏️ P2SHAWbQMT1UFX9Fb1nejhFo5DMbcK8Pt4ow7J

Merkle Root

9afa594f0300cef23df1cda6aa978e4d006b7b624a31da66c9aa692474a9ef9e
Transactions (1)
Coinbase9afa594f0300ce…aa692474a9ef9e
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.

4.606 Γ— 10⁹³(94-digit number)
46064498288018492704…33268839933151246091
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
4.606 Γ— 10⁹³(94-digit number)
46064498288018492704…33268839933151246091
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.212 Γ— 10⁹³(94-digit number)
92128996576036985408…66537679866302492181
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.842 Γ— 10⁹⁴(95-digit number)
18425799315207397081…33075359732604984361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.685 Γ— 10⁹⁴(95-digit number)
36851598630414794163…66150719465209968721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.370 Γ— 10⁹⁴(95-digit number)
73703197260829588327…32301438930419937441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.474 Γ— 10⁹⁡(96-digit number)
14740639452165917665…64602877860839874881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.948 Γ— 10⁹⁡(96-digit number)
29481278904331835330…29205755721679749761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.896 Γ— 10⁹⁡(96-digit number)
58962557808663670661…58411511443359499521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.179 Γ— 10⁹⁢(97-digit number)
11792511561732734132…16823022886718999041
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,726,387 XPMΒ·at block #6,810,288 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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