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Block #145,315

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/1/2013, 7:55:12 PM Β· Difficulty 9.8437 Β· 6,680,192 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0adba6f7542a860a4fbf994bfc4dcaa8ee9aeaf19e9647d2c882c6420ffb87b1
View on Chainz β†—

Height

#145,315

Difficulty

9.843695

Transactions

2

Size

1015 B

Version

2

Bits

09d7fc63

Nonce

181,590

Timestamp

9/1/2013, 7:55:12 PM

Confirmations

6,680,192

Mined by

⛏️ P2SHAXJXpeT6SoNdggwjeoV9Hh9zW3EkNjftUP

Merkle Root

97b3e17f7e279502bae293c72e057938a7532625e0407c21966582cca19ad810
Transactions (2)
Coinbase35559f50952324…c7545905ce5e6f
1 in β†’ 1 out10.3100 XPM109 B
AXJXpeT6…EkNjftUP
866a23f814e969…912523a7bbe919
5 in β†’ 2 out10.1964 XPM816 B
AKjttoj8…Q8PEHW53ARwRQL8j…mb3SXSrx
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.

1.971 Γ— 10⁹⁡(96-digit number)
19710512304372582873…62298609170429840001
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
1.971 Γ— 10⁹⁡(96-digit number)
19710512304372582873…62298609170429840001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.942 Γ— 10⁹⁡(96-digit number)
39421024608745165747…24597218340859680001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.884 Γ— 10⁹⁡(96-digit number)
78842049217490331495…49194436681719360001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.576 Γ— 10⁹⁢(97-digit number)
15768409843498066299…98388873363438720001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.153 Γ— 10⁹⁢(97-digit number)
31536819686996132598…96777746726877440001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.307 Γ— 10⁹⁢(97-digit number)
63073639373992265196…93555493453754880001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.261 Γ— 10⁹⁷(98-digit number)
12614727874798453039…87110986907509760001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.522 Γ— 10⁹⁷(98-digit number)
25229455749596906078…74221973815019520001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.045 Γ— 10⁹⁷(98-digit number)
50458911499193812157…48443947630039040001
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:57,848,153 XPMΒ·at block #6,825,506 Β· updates every 60s
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