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Block #159,028

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/10/2013, 8:04:46 PM Β· Difficulty 9.8656 Β· 6,658,963 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2b862065600582bc0ad9a47bf32b5326d9a164fcc8656f3f567ace6a16b1a024
View on Chainz β†—

Height

#159,028

Difficulty

9.865648

Transactions

1

Size

198 B

Version

2

Bits

09dd9b21

Nonce

340,106

Timestamp

9/10/2013, 8:04:46 PM

Confirmations

6,658,963

Mined by

⛏️ P2SHARwEjnekTmEd4gDgSnACXGZ9UNXN12RHSr

Merkle Root

a4c3659dc7d7a0bbed8c2b0f24a415516557d940a0c197de35ac8f62916b9932
Transactions (1)
Coinbasea4c3659dc7d7a0…ac8f62916b9932
1 in β†’ 1 out10.2600 XPM109 B
ARwEjnek…XN12RHSr
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.

3.045 Γ— 10⁹³(94-digit number)
30457691260418278484…51340152112158193281
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
3.045 Γ— 10⁹³(94-digit number)
30457691260418278484…51340152112158193281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.091 Γ— 10⁹³(94-digit number)
60915382520836556969…02680304224316386561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.218 Γ— 10⁹⁴(95-digit number)
12183076504167311393…05360608448632773121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.436 Γ— 10⁹⁴(95-digit number)
24366153008334622787…10721216897265546241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.873 Γ— 10⁹⁴(95-digit number)
48732306016669245575…21442433794531092481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.746 Γ— 10⁹⁴(95-digit number)
97464612033338491150…42884867589062184961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.949 Γ— 10⁹⁡(96-digit number)
19492922406667698230…85769735178124369921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.898 Γ— 10⁹⁡(96-digit number)
38985844813335396460…71539470356248739841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.797 Γ— 10⁹⁡(96-digit number)
77971689626670792920…43078940712497479681
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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