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Block #149,905

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/4/2013, 4:29:11 PM Β· Difficulty 9.8580 Β· 6,664,400 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
84b4a56fc721173063cdb68eb59e8d63d7bc205377d93dd8f94f05a1663b4a7d
View on Chainz β†—

Height

#149,905

Difficulty

9.858016

Transactions

2

Size

686 B

Version

2

Bits

09dba6ed

Nonce

127,714

Timestamp

9/4/2013, 4:29:11 PM

Confirmations

6,664,400

Mined by

⛏️ P2SHAbB3iyfpG81PRqK8LeT5oqng7LvApgHS2G

Merkle Root

11e5beab7a03a91e4458f6c8c1b45fc72126571e509f1a156e2b71f35c6c57f9
Transactions (2)
Coinbase2e811c87e75f2b…ec708280f783ce
1 in β†’ 1 out10.2859 XPM109 B
AbB3iyfp…vApgHS2G
9ef16829eb1e2a…95f05a9a3e67d1
3 in β†’ 1 out4.1000 XPM487 B
AYy6jDKp…aS5b1Ft6
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.

4.635 Γ— 10⁹⁡(96-digit number)
46350833419191502469…58785262864900288001
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
4.635 Γ— 10⁹⁡(96-digit number)
46350833419191502469…58785262864900288001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.270 Γ— 10⁹⁡(96-digit number)
92701666838383004938…17570525729800576001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.854 Γ— 10⁹⁢(97-digit number)
18540333367676600987…35141051459601152001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.708 Γ— 10⁹⁢(97-digit number)
37080666735353201975…70282102919202304001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.416 Γ— 10⁹⁢(97-digit number)
74161333470706403950…40564205838404608001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.483 Γ— 10⁹⁷(98-digit number)
14832266694141280790…81128411676809216001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.966 Γ— 10⁹⁷(98-digit number)
29664533388282561580…62256823353618432001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.932 Γ— 10⁹⁷(98-digit number)
59329066776565123160…24513646707236864001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.186 Γ— 10⁹⁸(99-digit number)
11865813355313024632…49027293414473728001
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:57,758,501 XPMΒ·at block #6,814,304 Β· updates every 60s
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