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Block #263,028

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/17/2013, 10:30:00 AM Β· Difficulty 9.9672 Β· 6,579,896 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
bef23fcbdf13672ed8287a9788acee367d30f6570687a8a3896504225c9ffdc7
View on Chainz β†—

Height

#263,028

Difficulty

9.967159

Transactions

1

Size

198 B

Version

2

Bits

09f797ba

Nonce

803,296

Timestamp

11/17/2013, 10:30:00 AM

Confirmations

6,579,896

Mined by

⛏️ P2SHAUpgzuCmZPRHmk6L4j2XXfHi1JkkPVcmYC

Merkle Root

6657a94c61ba0999dee2128577abcf752bc72a362427b98d42e192bbd40b81d3
Transactions (1)
Coinbase6657a94c61ba09…e192bbd40b81d3
1 in β†’ 1 out10.0500 XPM109 B
AUpgzuCm…kkPVcmYC
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.

3.414 Γ— 10⁹³(94-digit number)
34142595229850137681…12268683222192213701
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
3.414 Γ— 10⁹³(94-digit number)
34142595229850137681…12268683222192213701
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.828 Γ— 10⁹³(94-digit number)
68285190459700275362…24537366444384427401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.365 Γ— 10⁹⁴(95-digit number)
13657038091940055072…49074732888768854801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.731 Γ— 10⁹⁴(95-digit number)
27314076183880110144…98149465777537709601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.462 Γ— 10⁹⁴(95-digit number)
54628152367760220289…96298931555075419201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.092 Γ— 10⁹⁡(96-digit number)
10925630473552044057…92597863110150838401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.185 Γ— 10⁹⁡(96-digit number)
21851260947104088115…85195726220301676801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.370 Γ— 10⁹⁡(96-digit number)
43702521894208176231…70391452440603353601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.740 Γ— 10⁹⁡(96-digit number)
87405043788416352463…40782904881206707201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.748 Γ— 10⁹⁢(97-digit number)
17481008757683270492…81565809762413414401
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:57,987,740 XPMΒ·at block #6,842,923 Β· updates every 60s
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