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Block #30,138

2CCLength 7β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/13/2013, 6:00:36 PM Β· Difficulty 7.9862 Β· 6,794,969 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
663d49460b1a8f94b482b9e55141d32f8c3c72491da9627c80f9a06f078ded20
View on Chainz β†—

Height

#30,138

Difficulty

7.986235

Transactions

1

Size

198 B

Version

2

Bits

07fc79e6

Nonce

134

Timestamp

7/13/2013, 6:00:36 PM

Confirmations

6,794,969

Mined by

⛏️ P2SHAXciC8HNS9S5P5rEuP4DvtNMFMEX3Zpc3u

Merkle Root

292a43f8b930f99fb458aeeb9702e8222cd9385dfda6878b4a7e1e3661349014
Transactions (1)
Coinbase292a43f8b930f9…7e1e3661349014
1 in β†’ 1 out15.6600 XPM108 B
AXciC8HN…EX3Zpc3u
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.

6.871 Γ— 10⁹⁡(96-digit number)
68711141298960704391…75041246868187514111
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
6.871 Γ— 10⁹⁡(96-digit number)
68711141298960704391…75041246868187514111
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.374 Γ— 10⁹⁢(97-digit number)
13742228259792140878…50082493736375028221
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.748 Γ— 10⁹⁢(97-digit number)
27484456519584281756…00164987472750056441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.496 Γ— 10⁹⁢(97-digit number)
54968913039168563512…00329974945500112881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.099 Γ— 10⁹⁷(98-digit number)
10993782607833712702…00659949891000225761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.198 Γ— 10⁹⁷(98-digit number)
21987565215667425405…01319899782000451521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.397 Γ— 10⁹⁷(98-digit number)
43975130431334850810…02639799564000903041
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 7 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 7

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:57,844,939 XPMΒ·at block #6,825,106 Β· updates every 60s
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