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Block #230,504

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/27/2013, 8:28:03 PM Β· Difficulty 9.9397 Β· 6,578,856 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
49c9f0fc47e08adb55c5df1153808cddad3e5374a773d5ffc9e4061e474288d4
View on Chainz β†—

Height

#230,504

Difficulty

9.939732

Transactions

2

Size

540 B

Version

2

Bits

09f09245

Nonce

331,995

Timestamp

10/27/2013, 8:28:03 PM

Confirmations

6,578,856

Mined by

⛏️ P2SHAKgiTbagke9hfkPB2Na9G5N62UMJA8ujWZ

Merkle Root

fefb460fc8caae76f25dab327d657ee35f1d8e7e296868069e0e64851ba20950
Transactions (2)
Coinbase3be088fa04c704…20e3a0866c1950
1 in β†’ 1 out10.1200 XPM109 B
AKgiTbag…MJA8ujWZ
7f70fbe7b0d9b8…d5e898bbfe7053
2 in β†’ 1 out4.0456 XPM341 B
AKbyNwP5…Z1WicnvP
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.

2.813 Γ— 10⁹⁴(95-digit number)
28138721644516299087…74061517738951808001
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
2.813 Γ— 10⁹⁴(95-digit number)
28138721644516299087…74061517738951808001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.627 Γ— 10⁹⁴(95-digit number)
56277443289032598174…48123035477903616001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.125 Γ— 10⁹⁡(96-digit number)
11255488657806519634…96246070955807232001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.251 Γ— 10⁹⁡(96-digit number)
22510977315613039269…92492141911614464001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.502 Γ— 10⁹⁡(96-digit number)
45021954631226078539…84984283823228928001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.004 Γ— 10⁹⁡(96-digit number)
90043909262452157079…69968567646457856001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.800 Γ— 10⁹⁢(97-digit number)
18008781852490431415…39937135292915712001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.601 Γ— 10⁹⁢(97-digit number)
36017563704980862831…79874270585831424001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.203 Γ— 10⁹⁢(97-digit number)
72035127409961725663…59748541171662848001
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:57,718,948 XPMΒ·at block #6,809,359 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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