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Block #1,785,675

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/30/2016, 2:02:34 AM Β· Difficulty 10.7673 Β· 5,041,464 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
484bfe3af767b78fab70ced971400bde4c220261f1df9c6c211f579f908e415b
View on Chainz β†—

Height

#1,785,675

Difficulty

10.767306

Transactions

1

Size

199 B

Version

2

Bits

0ac46e27

Nonce

1,773,643,236

Timestamp

9/30/2016, 2:02:34 AM

Confirmations

5,041,464

Mined by

⛏️ P2SHAdAiPSoSjacKGSSgkEYgYdPKMmZrJzLfAu

Merkle Root

d1bc6d243d874c46376e751baa92df855961b5f01610828230595991e51baccd
Transactions (1)
Coinbased1bc6d243d874c…595991e51baccd
1 in β†’ 1 out8.6100 XPM109 B
AdAiPSoS…ZrJzLfAu
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.

3.871 Γ— 10⁹³(94-digit number)
38718913471109051913…09131167879576145501
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
3.871 Γ— 10⁹³(94-digit number)
38718913471109051913…09131167879576145501
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.743 Γ— 10⁹³(94-digit number)
77437826942218103826…18262335759152291001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.548 Γ— 10⁹⁴(95-digit number)
15487565388443620765…36524671518304582001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.097 Γ— 10⁹⁴(95-digit number)
30975130776887241530…73049343036609164001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.195 Γ— 10⁹⁴(95-digit number)
61950261553774483061…46098686073218328001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.239 Γ— 10⁹⁡(96-digit number)
12390052310754896612…92197372146436656001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.478 Γ— 10⁹⁡(96-digit number)
24780104621509793224…84394744292873312001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.956 Γ— 10⁹⁡(96-digit number)
49560209243019586449…68789488585746624001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.912 Γ— 10⁹⁡(96-digit number)
99120418486039172898…37578977171493248001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.982 Γ— 10⁹⁢(97-digit number)
19824083697207834579…75157954342986496001
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:57,861,293 XPMΒ·at block #6,827,138 Β· updates every 60s
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