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Block #229,364

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/27/2013, 3:43:45 AM Β· Difficulty 9.9380 Β· 6,615,980 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
06a086eef0c78af1e8c1b1ee67a4695d9e7206056f05aa2deb54e0cdfcac370f
View on Chainz β†—

Height

#229,364

Difficulty

9.938005

Transactions

1

Size

206 B

Version

2

Bits

09f02116

Nonce

1,558

Timestamp

10/27/2013, 3:43:45 AM

Confirmations

6,615,980

Mined by

⛏️ P2SHAcLBm5Z9BD7o7btAchFh9KZEkSS683d7c3

Merkle Root

5b534c0ec1454081d0ea757a8e81b82d689fecd428df0200d42c765576a446fa
Transactions (1)
Coinbase5b534c0ec14540…2c765576a446fa
1 in β†’ 1 out10.1100 XPM116 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.

2.428 Γ— 10⁹⁡(96-digit number)
24282615743312936016…67425016347954481961
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
2.428 Γ— 10⁹⁡(96-digit number)
24282615743312936016…67425016347954481961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.856 Γ— 10⁹⁡(96-digit number)
48565231486625872033…34850032695908963921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.713 Γ— 10⁹⁡(96-digit number)
97130462973251744067…69700065391817927841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.942 Γ— 10⁹⁢(97-digit number)
19426092594650348813…39400130783635855681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.885 Γ— 10⁹⁢(97-digit number)
38852185189300697627…78800261567271711361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.770 Γ— 10⁹⁢(97-digit number)
77704370378601395254…57600523134543422721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.554 Γ— 10⁹⁷(98-digit number)
15540874075720279050…15201046269086845441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.108 Γ— 10⁹⁷(98-digit number)
31081748151440558101…30402092538173690881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.216 Γ— 10⁹⁷(98-digit number)
62163496302881116203…60804185076347381761
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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