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Block #160,774

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/12/2013, 4:48:40 AM Β· Difficulty 9.8599 Β· 6,647,320 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2dd35f9117054e2ae61db2e32a46c6cb63cb743f2943d1ad30c3da6cb555c354
View on Chainz β†—

Height

#160,774

Difficulty

9.859860

Transactions

1

Size

198 B

Version

2

Bits

09dc1fcb

Nonce

355,442

Timestamp

9/12/2013, 4:48:40 AM

Confirmations

6,647,320

Mined by

⛏️ P2SHAWbm4AWfhyZEMkdPYLMs4FyYdBzNGrUw91

Merkle Root

b125627bb4b63b519873bcf7364c5a7009d663b6c14858c0f754cea58dfa6dd6
Transactions (1)
Coinbaseb125627bb4b63b…54cea58dfa6dd6
1 in β†’ 1 out10.2700 XPM109 B
AWbm4AWf…zNGrUw91
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.

2.492 Γ— 10⁹³(94-digit number)
24923111975055341215…93831260581311471501
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
2.492 Γ— 10⁹³(94-digit number)
24923111975055341215…93831260581311471501
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.984 Γ— 10⁹³(94-digit number)
49846223950110682430…87662521162622943001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.969 Γ— 10⁹³(94-digit number)
99692447900221364860…75325042325245886001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.993 Γ— 10⁹⁴(95-digit number)
19938489580044272972…50650084650491772001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.987 Γ— 10⁹⁴(95-digit number)
39876979160088545944…01300169300983544001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.975 Γ— 10⁹⁴(95-digit number)
79753958320177091888…02600338601967088001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.595 Γ— 10⁹⁡(96-digit number)
15950791664035418377…05200677203934176001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.190 Γ— 10⁹⁡(96-digit number)
31901583328070836755…10401354407868352001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.380 Γ— 10⁹⁡(96-digit number)
63803166656141673510…20802708815736704001
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:57,708,798 XPMΒ·at block #6,808,093 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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