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Block #504,020

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/21/2014, 12:33:23 PM Β· Difficulty 10.8077 Β· 6,320,822 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d3a7ecd84e3b44fed33e45bea1e957c86d88e890f82b9af7715fde8d97627046
View on Chainz β†—

Height

#504,020

Difficulty

10.807694

Transactions

1

Size

200 B

Version

2

Bits

0acec510

Nonce

6,148,207

Timestamp

4/21/2014, 12:33:23 PM

Confirmations

6,320,822

Mined by

⛏️ P2SHAKwbR11RwaeGbuAPkpMhxrEzDZQd9vd1LZ

Merkle Root

287190995bfcf3acf5b617a3284fef6584137ee178af86c4d4810525a9636fcd
Transactions (1)
Coinbase287190995bfcf3…810525a9636fcd
1 in β†’ 1 out8.5500 XPM109 B
AKwbR11R…Qd9vd1LZ
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.

4.849 Γ— 10⁹⁢(97-digit number)
48491446224989138034…42426236342822543361
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
4.849 Γ— 10⁹⁢(97-digit number)
48491446224989138034…42426236342822543361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.698 Γ— 10⁹⁢(97-digit number)
96982892449978276068…84852472685645086721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.939 Γ— 10⁹⁷(98-digit number)
19396578489995655213…69704945371290173441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.879 Γ— 10⁹⁷(98-digit number)
38793156979991310427…39409890742580346881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.758 Γ— 10⁹⁷(98-digit number)
77586313959982620855…78819781485160693761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.551 Γ— 10⁹⁸(99-digit number)
15517262791996524171…57639562970321387521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.103 Γ— 10⁹⁸(99-digit number)
31034525583993048342…15279125940642775041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.206 Γ— 10⁹⁸(99-digit number)
62069051167986096684…30558251881285550081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.241 Γ— 10⁹⁹(100-digit number)
12413810233597219336…61116503762571100161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.482 Γ— 10⁹⁹(100-digit number)
24827620467194438673…22233007525142200321
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:57,842,816 XPMΒ·at block #6,824,841 Β· updates every 60s
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