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Block #375,534

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/25/2014, 6:55:51 PM Β· Difficulty 10.4241 Β· 6,427,167 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0ab8e73bcd08443bc94491b7a3c7ecd9447161e5f53889c92f8e7298f0f27c83
View on Chainz β†—

Height

#375,534

Difficulty

10.424141

Transactions

1

Size

210 B

Version

2

Bits

0a6c947d

Nonce

931,055

Timestamp

1/25/2014, 6:55:51 PM

Confirmations

6,427,167

Mined by

⛏️ P2SHAW6FdqAF2QFTdoj8WBd1FEKDKLmbtgXE2r

Merkle Root

2157949e144c8aaed6ead9ac5fb7388fe7982c7eae67a28dfe3da5f74674d21c
Transactions (1)
Coinbase2157949e144c8a…3da5f74674d21c
1 in β†’ 1 out9.1900 XPM118 B
AW6FdqAF…mbtgXE2r
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.

4.233 Γ— 10⁹⁸(99-digit number)
42330852533650123505…67496029183674613761
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
4.233 Γ— 10⁹⁸(99-digit number)
42330852533650123505…67496029183674613761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.466 Γ— 10⁹⁸(99-digit number)
84661705067300247011…34992058367349227521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.693 Γ— 10⁹⁹(100-digit number)
16932341013460049402…69984116734698455041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.386 Γ— 10⁹⁹(100-digit number)
33864682026920098804…39968233469396910081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.772 Γ— 10⁹⁹(100-digit number)
67729364053840197609…79936466938793820161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.354 Γ— 10¹⁰⁰(101-digit number)
13545872810768039521…59872933877587640321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.709 Γ— 10¹⁰⁰(101-digit number)
27091745621536079043…19745867755175280641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.418 Γ— 10¹⁰⁰(101-digit number)
54183491243072158087…39491735510350561281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.083 Γ— 10¹⁰¹(102-digit number)
10836698248614431617…78983471020701122561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.167 Γ— 10¹⁰¹(102-digit number)
21673396497228863235…57966942041402245121
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:57,665,632 XPMΒ·at block #6,802,700 Β· updates every 60s
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