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Block #176,585

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/23/2013, 1:26:27 AM Β· Difficulty 9.8654 Β· 6,629,677 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
564822311fa37af099c7c32e03a524c54550daa490da105752fba47c2feef4b6
View on Chainz β†—

Height

#176,585

Difficulty

9.865396

Transactions

1

Size

197 B

Version

2

Bits

09dd8a97

Nonce

38,757

Timestamp

9/23/2013, 1:26:27 AM

Confirmations

6,629,677

Mined by

⛏️ P2SHALefmcuDW4F9iECbUGXjGP8npv6bSfgMPT

Merkle Root

80819b88af6774b421cd6380f800f552d3da715ab78e9a4aab7d7e3367fe4ca5
Transactions (1)
Coinbase80819b88af6774…7d7e3367fe4ca5
1 in β†’ 1 out10.2600 XPM109 B
ALefmcuD…6bSfgMPT
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.

7.459 Γ— 10⁸⁸(89-digit number)
74595863002326391884…66662409570088418641
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
7.459 Γ— 10⁸⁸(89-digit number)
74595863002326391884…66662409570088418641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.491 Γ— 10⁸⁹(90-digit number)
14919172600465278376…33324819140176837281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.983 Γ— 10⁸⁹(90-digit number)
29838345200930556753…66649638280353674561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.967 Γ— 10⁸⁹(90-digit number)
59676690401861113507…33299276560707349121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.193 Γ— 10⁹⁰(91-digit number)
11935338080372222701…66598553121414698241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.387 Γ— 10⁹⁰(91-digit number)
23870676160744445403…33197106242829396481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.774 Γ— 10⁹⁰(91-digit number)
47741352321488890806…66394212485658792961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.548 Γ— 10⁹⁰(91-digit number)
95482704642977781612…32788424971317585921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.909 Γ— 10⁹¹(92-digit number)
19096540928595556322…65576849942635171841
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:57,694,180 XPMΒ·at block #6,806,261 Β· updates every 60s
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