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Block #533,864

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/9/2014, 11:13:32 PM Β· Difficulty 10.9009 Β· 6,275,379 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c1668c17541dda72db36eeafed143dccc570d28ea449d33af379d23ba62e218e
View on Chainz β†—

Height

#533,864

Difficulty

10.900946

Transactions

1

Size

208 B

Version

2

Bits

0ae6a46d

Nonce

123,416,073

Timestamp

5/9/2014, 11:13:32 PM

Confirmations

6,275,379

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

4a7ea0d2940e46b4c76cb824fd3d884620d4258cb2003766f1171d010716742c
Transactions (1)
Coinbase4a7ea0d2940e46…171d010716742c
1 in β†’ 1 out8.4000 XPM116 B
ANSXnLY2…Sd25TjkD
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.

1.687 Γ— 10⁹⁹(100-digit number)
16879658156060719598…43830754016918168161
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
1.687 Γ— 10⁹⁹(100-digit number)
16879658156060719598…43830754016918168161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.375 Γ— 10⁹⁹(100-digit number)
33759316312121439197…87661508033836336321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.751 Γ— 10⁹⁹(100-digit number)
67518632624242878395…75323016067672672641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.350 Γ— 10¹⁰⁰(101-digit number)
13503726524848575679…50646032135345345281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.700 Γ— 10¹⁰⁰(101-digit number)
27007453049697151358…01292064270690690561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.401 Γ— 10¹⁰⁰(101-digit number)
54014906099394302716…02584128541381381121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.080 Γ— 10¹⁰¹(102-digit number)
10802981219878860543…05168257082762762241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.160 Γ— 10¹⁰¹(102-digit number)
21605962439757721086…10336514165525524481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.321 Γ— 10¹⁰¹(102-digit number)
43211924879515442173…20673028331051048961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
8.642 Γ— 10¹⁰¹(102-digit number)
86423849759030884346…41346056662102097921
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:57,718,009 XPMΒ·at block #6,809,242 Β· updates every 60s
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