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Block #165,179

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/15/2013, 2:57:50 AM Β· Difficulty 9.8653 Β· 6,633,111 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
25897706172f10381f0a341dc07158d9bbc851833b54c6c60100145309cc0761
View on Chainz β†—

Height

#165,179

Difficulty

9.865324

Transactions

3

Size

517 B

Version

2

Bits

09dd85de

Nonce

72,905

Timestamp

9/15/2013, 2:57:50 AM

Confirmations

6,633,111

Mined by

⛏️ P2SHAGtiYkzRzPqqXVAsPkt4YctCi6Xq14yS4j

Merkle Root

d82c334149150e12cd4d621f24bcc0ec702d2368423658dc8b30fa06739f5fa4
Transactions (3)
Coinbase1d1cbd74c88075…5012a4e18bc9f3
1 in β†’ 1 out10.2800 XPM109 B
AGtiYkzR…Xq14yS4j
62aca8eab5f717…d993b83a519254
1 in β†’ 1 out10.2600 XPM159 B
AeTde7fH…w7crTzqr
f529b6364a30e5…bc006701d5ae4d
1 in β†’ 1 out10.2600 XPM158 B
AeTde7fH…w7crTzqr
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.

7.785 Γ— 10⁹⁡(96-digit number)
77856368518997572042…02047374241451443601
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
7.785 Γ— 10⁹⁡(96-digit number)
77856368518997572042…02047374241451443601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.557 Γ— 10⁹⁢(97-digit number)
15571273703799514408…04094748482902887201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.114 Γ— 10⁹⁢(97-digit number)
31142547407599028817…08189496965805774401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.228 Γ— 10⁹⁢(97-digit number)
62285094815198057634…16378993931611548801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.245 Γ— 10⁹⁷(98-digit number)
12457018963039611526…32757987863223097601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.491 Γ— 10⁹⁷(98-digit number)
24914037926079223053…65515975726446195201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.982 Γ— 10⁹⁷(98-digit number)
49828075852158446107…31031951452892390401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.965 Γ— 10⁹⁷(98-digit number)
99656151704316892214…62063902905784780801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.993 Γ— 10⁹⁸(99-digit number)
19931230340863378442…24127805811569561601
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:57,630,323 XPMΒ·at block #6,798,289 Β· updates every 60s
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