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Block #176,930

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/23/2013, 7:16:00 AM Β· Difficulty 9.8654 Β· 6,638,214 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8ac1c371116c829750e3c7bdc1d6d46d9078cf70976387a36dc724b7b4c81478
View on Chainz β†—

Height

#176,930

Difficulty

9.865420

Transactions

1

Size

200 B

Version

2

Bits

09dd8c2f

Nonce

393,595

Timestamp

9/23/2013, 7:16:00 AM

Confirmations

6,638,214

Mined by

⛏️ P2SHAG985DnznTo6esPQLjXLAh36pqz3fiYGsJ

Merkle Root

25c43194432453fa043c723c4dd111b4a00138d2e39da38f7a7ea6e404b86681
Transactions (1)
Coinbase25c43194432453…7ea6e404b86681
1 in β†’ 1 out10.2600 XPM109 B
AG985Dnz…z3fiYGsJ
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.

4.861 Γ— 10⁹⁷(98-digit number)
48614059958724018744…45240411953007554561
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
4.861 Γ— 10⁹⁷(98-digit number)
48614059958724018744…45240411953007554561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.722 Γ— 10⁹⁷(98-digit number)
97228119917448037489…90480823906015109121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.944 Γ— 10⁹⁸(99-digit number)
19445623983489607497…80961647812030218241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.889 Γ— 10⁹⁸(99-digit number)
38891247966979214995…61923295624060436481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.778 Γ— 10⁹⁸(99-digit number)
77782495933958429991…23846591248120872961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.555 Γ— 10⁹⁹(100-digit number)
15556499186791685998…47693182496241745921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.111 Γ— 10⁹⁹(100-digit number)
31112998373583371996…95386364992483491841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.222 Γ— 10⁹⁹(100-digit number)
62225996747166743993…90772729984966983681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.244 Γ— 10¹⁰⁰(101-digit number)
12445199349433348798…81545459969933967361
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:57,765,246 XPMΒ·at block #6,815,143 Β· updates every 60s
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