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Block #245,382

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/5/2013, 10:35:22 AM Β· Difficulty 9.9639 Β· 6,581,754 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
51c35024551fdfcbc0185aa6d389dc053ebd247a63261bf29767ec28949e623b
View on Chainz β†—

Height

#245,382

Difficulty

9.963887

Transactions

1

Size

198 B

Version

2

Bits

09f6c14f

Nonce

3,580

Timestamp

11/5/2013, 10:35:22 AM

Confirmations

6,581,754

Mined by

⛏️ P2SHAYDZhi2ATcpB6cf15iGzieKf1815tJmJHB

Merkle Root

42b9b015c25b81417f1774953f125330947384da1dca22e3f4459a3fddc98fef
Transactions (1)
Coinbase42b9b015c25b81…459a3fddc98fef
1 in β†’ 1 out10.0600 XPM109 B
AYDZhi2A…15tJmJHB
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.

7.720 Γ— 10⁹²(93-digit number)
77201191693581941866…69846564188854688001
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
7.720 Γ— 10⁹²(93-digit number)
77201191693581941866…69846564188854688001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.544 Γ— 10⁹³(94-digit number)
15440238338716388373…39693128377709376001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.088 Γ— 10⁹³(94-digit number)
30880476677432776746…79386256755418752001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.176 Γ— 10⁹³(94-digit number)
61760953354865553492…58772513510837504001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.235 Γ— 10⁹⁴(95-digit number)
12352190670973110698…17545027021675008001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.470 Γ— 10⁹⁴(95-digit number)
24704381341946221397…35090054043350016001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.940 Γ— 10⁹⁴(95-digit number)
49408762683892442794…70180108086700032001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.881 Γ— 10⁹⁴(95-digit number)
98817525367784885588…40360216173400064001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.976 Γ— 10⁹⁡(96-digit number)
19763505073556977117…80720432346800128001
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
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