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Block #172,045

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/19/2013, 10:41:57 PM Β· Difficulty 9.8637 Β· 6,645,317 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6395a6a9ed36a333af013f50ff198902e0899d1386c33c040fe733ff7d9fb424
View on Chainz β†—

Height

#172,045

Difficulty

9.863654

Transactions

1

Size

198 B

Version

2

Bits

09dd1871

Nonce

126,028

Timestamp

9/19/2013, 10:41:57 PM

Confirmations

6,645,317

Mined by

⛏️ P2SHAWKimBPMQT8AEeEuQZ96qGCDXD2EpmG96V

Merkle Root

24e78ef573d5d8a540e05c877e431a42fef49aaa4ee9087b36f68123301a33c8
Transactions (1)
Coinbase24e78ef573d5d8…f68123301a33c8
1 in β†’ 1 out10.2600 XPM109 B
AWKimBPM…2EpmG96V
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.

5.413 Γ— 10⁹²(93-digit number)
54130616887849521263…75847883135186290401
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
5.413 Γ— 10⁹²(93-digit number)
54130616887849521263…75847883135186290401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.082 Γ— 10⁹³(94-digit number)
10826123377569904252…51695766270372580801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.165 Γ— 10⁹³(94-digit number)
21652246755139808505…03391532540745161601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.330 Γ— 10⁹³(94-digit number)
43304493510279617011…06783065081490323201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.660 Γ— 10⁹³(94-digit number)
86608987020559234022…13566130162980646401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.732 Γ— 10⁹⁴(95-digit number)
17321797404111846804…27132260325961292801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.464 Γ— 10⁹⁴(95-digit number)
34643594808223693608…54264520651922585601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.928 Γ— 10⁹⁴(95-digit number)
69287189616447387217…08529041303845171201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.385 Γ— 10⁹⁡(96-digit number)
13857437923289477443…17058082607690342401
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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