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Block #365,225

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/18/2014, 2:40:53 PM Β· Difficulty 10.4239 Β· 6,437,278 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
422f096ff6a308666b653ceb07ea5fe52b530512de9bc9b84e89f07d4ab1dac5
View on Chainz β†—

Height

#365,225

Difficulty

10.423944

Transactions

1

Size

201 B

Version

2

Bits

0a6c879d

Nonce

410,640

Timestamp

1/18/2014, 2:40:53 PM

Confirmations

6,437,278

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

9b6c3a70881ad6e1a721a519fb818d6d800a256e831e0e8a72d4950e129c356a
Transactions (1)
Coinbase9b6c3a70881ad6…d4950e129c356a
1 in β†’ 1 out9.1900 XPM110 B
AeKNrjNj…1NEq95Ta
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.

1.510 Γ— 10⁹⁷(98-digit number)
15106417466963022474…50757339820281623041
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
1.510 Γ— 10⁹⁷(98-digit number)
15106417466963022474…50757339820281623041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.021 Γ— 10⁹⁷(98-digit number)
30212834933926044948…01514679640563246081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.042 Γ— 10⁹⁷(98-digit number)
60425669867852089896…03029359281126492161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.208 Γ— 10⁹⁸(99-digit number)
12085133973570417979…06058718562252984321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.417 Γ— 10⁹⁸(99-digit number)
24170267947140835958…12117437124505968641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.834 Γ— 10⁹⁸(99-digit number)
48340535894281671917…24234874249011937281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.668 Γ— 10⁹⁸(99-digit number)
96681071788563343834…48469748498023874561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.933 Γ— 10⁹⁹(100-digit number)
19336214357712668766…96939496996047749121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.867 Γ— 10⁹⁹(100-digit number)
38672428715425337533…93878993992095498241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.734 Γ— 10⁹⁹(100-digit number)
77344857430850675067…87757987984190996481
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:57,664,033 XPMΒ·at block #6,802,502 Β· updates every 60s
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