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Block #537,571

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/11/2014, 10:49:53 PM Β· Difficulty 10.9165 Β· 6,275,235 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b3641a1db374dbfee983b93a7ed4f6dbd5ac67b3567bd2677d5dc71a85c106b9
View on Chainz β†—

Height

#537,571

Difficulty

10.916501

Transactions

3

Size

1.36 KB

Version

2

Bits

0aea9fcc

Nonce

386,526

Timestamp

5/11/2014, 10:49:53 PM

Confirmations

6,275,235

Mined by

⛏️ P2SHAcH2s7Y4D9hVCSQQdA7jo9e2ue1nk8yDe6

Merkle Root

12272f07a08d7da9e3bca1a63e5134ee69aa3e84a98362a1741855fcd18fc8b5
Transactions (3)
Coinbase7864650e55ac6e…b4690abd01f7ca
1 in β†’ 1 out8.4000 XPM109 B
AcH2s7Y4…1nk8yDe6
79854ad6e161d9…11064be969eb17
6 in β†’ 2 out7.1145 XPM964 B
AXcdn6Q4…S8jA3aH8AJzeuA7Q…Fq9xpimj
77d628f09085b5…8997dd05f20bef
1 in β†’ 2 out5.3751 XPM226 B
AWkTY9wW…HrBW1npqAeKNrjNj…1NEq95Ta
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.

9.381 Γ— 10⁹⁢(97-digit number)
93813632865518239196…91461587337080571681
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
9.381 Γ— 10⁹⁢(97-digit number)
93813632865518239196…91461587337080571681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.876 Γ— 10⁹⁷(98-digit number)
18762726573103647839…82923174674161143361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.752 Γ— 10⁹⁷(98-digit number)
37525453146207295678…65846349348322286721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.505 Γ— 10⁹⁷(98-digit number)
75050906292414591357…31692698696644573441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.501 Γ— 10⁹⁸(99-digit number)
15010181258482918271…63385397393289146881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.002 Γ— 10⁹⁸(99-digit number)
30020362516965836542…26770794786578293761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.004 Γ— 10⁹⁸(99-digit number)
60040725033931673085…53541589573156587521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.200 Γ— 10⁹⁹(100-digit number)
12008145006786334617…07083179146313175041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.401 Γ— 10⁹⁹(100-digit number)
24016290013572669234…14166358292626350081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.803 Γ— 10⁹⁹(100-digit number)
48032580027145338468…28332716585252700161
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:47,754,209 XPMΒ·at block #6,812,805 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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