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Block #157,029

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/9/2013, 8:46:32 AM Β· Difficulty 9.8687 Β· 6,647,980 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b1f1a22d107ee2f4383a38320381afcf5671ea0ae1cc600820488915c374977d
View on Chainz β†—

Height

#157,029

Difficulty

9.868697

Transactions

1

Size

197 B

Version

2

Bits

09de62f0

Nonce

5,044

Timestamp

9/9/2013, 8:46:32 AM

Confirmations

6,647,980

Mined by

⛏️ P2SHAP91QEDQfufBUohT6sogfnRJN9W6JZAB9n

Merkle Root

73b284800414f4f5be04f035ac82d10f6d7309a66c8ec4a2585b460a56749cab
Transactions (1)
Coinbase73b284800414f4…5b460a56749cab
1 in β†’ 1 out10.2500 XPM109 B
AP91QEDQ…W6JZAB9n
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.

3.803 Γ— 10⁹⁰(91-digit number)
38033747670123513215…00395132335519715201
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
3.803 Γ— 10⁹⁰(91-digit number)
38033747670123513215…00395132335519715201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.606 Γ— 10⁹⁰(91-digit number)
76067495340247026431…00790264671039430401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.521 Γ— 10⁹¹(92-digit number)
15213499068049405286…01580529342078860801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.042 Γ— 10⁹¹(92-digit number)
30426998136098810572…03161058684157721601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.085 Γ— 10⁹¹(92-digit number)
60853996272197621144…06322117368315443201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.217 Γ— 10⁹²(93-digit number)
12170799254439524228…12644234736630886401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.434 Γ— 10⁹²(93-digit number)
24341598508879048457…25288469473261772801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.868 Γ— 10⁹²(93-digit number)
48683197017758096915…50576938946523545601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.736 Γ— 10⁹²(93-digit number)
97366394035516193831…01153877893047091201
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:57,684,141 XPMΒ·at block #6,805,008 Β· updates every 60s
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