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Block #162,917

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/13/2013, 3:25:31 PM Β· Difficulty 9.8617 Β· 6,653,838 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
64ae97e9f3045e361b4333709e38b34c528f9d00c8089132e75a05650bb48311
View on Chainz β†—

Height

#162,917

Difficulty

9.861712

Transactions

1

Size

199 B

Version

2

Bits

09dc9922

Nonce

73,718

Timestamp

9/13/2013, 3:25:31 PM

Confirmations

6,653,838

Mined by

⛏️ P2SHARwEjnekTmEd4gDgSnACXGZ9UNXN12RHSr

Merkle Root

ac995b05c5cc50bd9d3a840b431a8ef9503b4e41ad4a63abc2f045901b5afdef
Transactions (1)
Coinbaseac995b05c5cc50…f045901b5afdef
1 in β†’ 1 out10.2700 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.

9.373 Γ— 10⁹⁴(95-digit number)
93730573725461729312…14726549595907612541
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
9.373 Γ— 10⁹⁴(95-digit number)
93730573725461729312…14726549595907612541
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.874 Γ— 10⁹⁡(96-digit number)
18746114745092345862…29453099191815225081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.749 Γ— 10⁹⁡(96-digit number)
37492229490184691724…58906198383630450161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.498 Γ— 10⁹⁡(96-digit number)
74984458980369383449…17812396767260900321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.499 Γ— 10⁹⁢(97-digit number)
14996891796073876689…35624793534521800641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.999 Γ— 10⁹⁢(97-digit number)
29993783592147753379…71249587069043601281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.998 Γ— 10⁹⁢(97-digit number)
59987567184295506759…42499174138087202561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.199 Γ— 10⁹⁷(98-digit number)
11997513436859101351…84998348276174405121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.399 Γ— 10⁹⁷(98-digit number)
23995026873718202703…69996696552348810241
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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