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Block #2,084,320

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/23/2017, 1:32:40 PM Β· Difficulty 10.8726 Β· 4,757,511 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f57535f2e5b41de035230c4988cb1d0c01a3f24e7672a056de3f8089308b2173
View on Chainz β†—

Height

#2,084,320

Difficulty

10.872608

Transactions

1

Size

199 B

Version

2

Bits

0adf633b

Nonce

1,258,995,531

Timestamp

4/23/2017, 1:32:40 PM

Confirmations

4,757,511

Mined by

⛏️ P2SHATXN3YQ1mj7jwCRiijECzrhSrCgHcWR77A

Merkle Root

1eef6fdc47f7f78edcf047aa295af7c86ab722dd1ae8d206cba87f4216b4ebfb
Transactions (1)
Coinbase1eef6fdc47f7f7…a87f4216b4ebfb
1 in β†’ 1 out8.4500 XPM109 B
ATXN3YQ1…gHcWR77A
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.

3.999 Γ— 10⁹⁡(96-digit number)
39993588953709329365…40712799238602630401
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
3.999 Γ— 10⁹⁡(96-digit number)
39993588953709329365…40712799238602630401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.998 Γ— 10⁹⁡(96-digit number)
79987177907418658730…81425598477205260801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.599 Γ— 10⁹⁢(97-digit number)
15997435581483731746…62851196954410521601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.199 Γ— 10⁹⁢(97-digit number)
31994871162967463492…25702393908821043201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.398 Γ— 10⁹⁢(97-digit number)
63989742325934926984…51404787817642086401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.279 Γ— 10⁹⁷(98-digit number)
12797948465186985396…02809575635284172801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.559 Γ— 10⁹⁷(98-digit number)
25595896930373970793…05619151270568345601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.119 Γ— 10⁹⁷(98-digit number)
51191793860747941587…11238302541136691201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.023 Γ— 10⁹⁸(99-digit number)
10238358772149588317…22476605082273382401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.047 Γ— 10⁹⁸(99-digit number)
20476717544299176635…44953210164546764801
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:57,979,022 XPMΒ·at block #6,841,830 Β· updates every 60s
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