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Block #146,154

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/2/2013, 8:12:56 AM Β· Difficulty 9.8467 Β· 6,668,145 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
09c17e44b0aa9d4e4dc5ffeb0697515b89629e549f5835ca92e06e0bb9693aaa
View on Chainz β†—

Height

#146,154

Difficulty

9.846739

Transactions

1

Size

198 B

Version

2

Bits

09d8c3e1

Nonce

23,146

Timestamp

9/2/2013, 8:12:56 AM

Confirmations

6,668,145

Mined by

⛏️ P2SHASki8pmAYiSmpQcpe6L3Yu14B9Dwetzr7b

Merkle Root

4fccdce75a9272c143e396f72fc9c30be9d8637491b7cc6d7f9efa6a5c8a7f3b
Transactions (1)
Coinbase4fccdce75a9272…9efa6a5c8a7f3b
1 in β†’ 1 out10.3000 XPM109 B
ASki8pmA…Dwetzr7b
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.

1.168 Γ— 10⁹²(93-digit number)
11687857269143761047…73220868779351577601
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
1.168 Γ— 10⁹²(93-digit number)
11687857269143761047…73220868779351577601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.337 Γ— 10⁹²(93-digit number)
23375714538287522095…46441737558703155201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.675 Γ— 10⁹²(93-digit number)
46751429076575044190…92883475117406310401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.350 Γ— 10⁹²(93-digit number)
93502858153150088380…85766950234812620801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.870 Γ— 10⁹³(94-digit number)
18700571630630017676…71533900469625241601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.740 Γ— 10⁹³(94-digit number)
37401143261260035352…43067800939250483201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.480 Γ— 10⁹³(94-digit number)
74802286522520070704…86135601878500966401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.496 Γ— 10⁹⁴(95-digit number)
14960457304504014140…72271203757001932801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.992 Γ— 10⁹⁴(95-digit number)
29920914609008028281…44542407514003865601
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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