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Block #450,308

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/19/2014, 5:33:33 AM Β· Difficulty 10.3695 Β· 6,346,077 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3e660027c5624cd8117cde6a5f965a521df6e60bbaf6ff24ca0e3cad17981fbc
View on Chainz β†—

Height

#450,308

Difficulty

10.369503

Transactions

2

Size

395 B

Version

2

Bits

0a5e97bc

Nonce

25,766

Timestamp

3/19/2014, 5:33:33 AM

Confirmations

6,346,077

Mined by

⛏️ P2SHAecZSL8qqeR7WubRX5vqZWFTKEWCPbB7Mh

Merkle Root

12dd0d5933f437a7d757806dfb24d709218e6b8eccafb2c81db5611c8c5f1412
Transactions (2)
Coinbase6b5a9bbba98862…1e5bdf3b2c5a46
1 in β†’ 1 out9.3000 XPM111 B
AecZSL8q…WCPbB7Mh
d5b47a86a29e29…7f33e4ec531755
1 in β†’ 1 out15.0900 XPM193 B
Ad8U58R8…SHTr1XuA
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.

1.877 Γ— 10⁹⁸(99-digit number)
18774421045389150738…64114363128967941041
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
1.877 Γ— 10⁹⁸(99-digit number)
18774421045389150738…64114363128967941041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.754 Γ— 10⁹⁸(99-digit number)
37548842090778301476…28228726257935882081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.509 Γ— 10⁹⁸(99-digit number)
75097684181556602953…56457452515871764161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.501 Γ— 10⁹⁹(100-digit number)
15019536836311320590…12914905031743528321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.003 Γ— 10⁹⁹(100-digit number)
30039073672622641181…25829810063487056641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.007 Γ— 10⁹⁹(100-digit number)
60078147345245282362…51659620126974113281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.201 Γ— 10¹⁰⁰(101-digit number)
12015629469049056472…03319240253948226561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.403 Γ— 10¹⁰⁰(101-digit number)
24031258938098112945…06638480507896453121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.806 Γ— 10¹⁰⁰(101-digit number)
48062517876196225890…13276961015792906241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
9.612 Γ— 10¹⁰⁰(101-digit number)
96125035752392451780…26553922031585812481
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:57,615,077 XPMΒ·at block #6,796,384 Β· updates every 60s
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