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Block #173,773

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/21/2013, 5:55:45 AM Β· Difficulty 9.8598 Β· 6,643,035 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
364c1fc4e1aad4dc2dfc2969a8d09ca3ed1792c1695d2de9bb8f87c35434db8c
View on Chainz β†—

Height

#173,773

Difficulty

9.859845

Transactions

1

Size

200 B

Version

2

Bits

09dc1ecd

Nonce

973,080,279

Timestamp

9/21/2013, 5:55:45 AM

Confirmations

6,643,035

Mined by

⛏️ P2SHAcLBm5Z9BD7o7btAchFh9KZEkSS683d7c3

Merkle Root

1a8241f75b58a6682d3eaec9512dacf459c19b467f7ad9f067c2cf6274dfa8e1
Transactions (1)
Coinbase1a8241f75b58a6…c2cf6274dfa8e1
1 in β†’ 1 out10.2700 XPM112 B
AcLBm5Z9…S683d7c3
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.

5.824 Γ— 10⁸⁹(90-digit number)
58246126400533181377…22761430236310875921
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
5.824 Γ— 10⁸⁹(90-digit number)
58246126400533181377…22761430236310875921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.164 Γ— 10⁹⁰(91-digit number)
11649225280106636275…45522860472621751841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.329 Γ— 10⁹⁰(91-digit number)
23298450560213272550…91045720945243503681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.659 Γ— 10⁹⁰(91-digit number)
46596901120426545101…82091441890487007361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.319 Γ— 10⁹⁰(91-digit number)
93193802240853090203…64182883780974014721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.863 Γ— 10⁹¹(92-digit number)
18638760448170618040…28365767561948029441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.727 Γ— 10⁹¹(92-digit number)
37277520896341236081…56731535123896058881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.455 Γ— 10⁹¹(92-digit number)
74555041792682472163…13463070247792117761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.491 Γ— 10⁹²(93-digit number)
14911008358536494432…26926140495584235521
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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