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Block #456,240

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/23/2014, 2:18:09 AM Β· Difficulty 10.4166 Β· 6,339,596 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
00c8107d9f8fb5458001a8ff96bf4b32c6b4fb4e86eb5fa8e24c4a0c2bc9d180
View on Chainz β†—

Height

#456,240

Difficulty

10.416571

Transactions

1

Size

199 B

Version

2

Bits

0a6aa46c

Nonce

1,068,337,798

Timestamp

3/23/2014, 2:18:09 AM

Confirmations

6,339,596

Mined by

⛏️ P2SHAU4oUk2VxF9MFDkFs15mpXMBvscfyhJaJ8

Merkle Root

65dd4df745bbd7b06ba615f0c7b84cb03d44d8999a312574bdbdf57f56bcfe5b
Transactions (1)
Coinbase65dd4df745bbd7…bdf57f56bcfe5b
1 in β†’ 1 out9.2000 XPM109 B
AU4oUk2V…cfyhJaJ8
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.

3.136 Γ— 10⁹⁴(95-digit number)
31360637630090855273…60948847376915369779
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
3.136 Γ— 10⁹⁴(95-digit number)
31360637630090855273…60948847376915369779
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.272 Γ— 10⁹⁴(95-digit number)
62721275260181710546…21897694753830739559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.254 Γ— 10⁹⁡(96-digit number)
12544255052036342109…43795389507661479119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.508 Γ— 10⁹⁡(96-digit number)
25088510104072684218…87590779015322958239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.017 Γ— 10⁹⁡(96-digit number)
50177020208145368436…75181558030645916479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.003 Γ— 10⁹⁢(97-digit number)
10035404041629073687…50363116061291832959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.007 Γ— 10⁹⁢(97-digit number)
20070808083258147374…00726232122583665919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.014 Γ— 10⁹⁢(97-digit number)
40141616166516294749…01452464245167331839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.028 Γ— 10⁹⁢(97-digit number)
80283232333032589499…02904928490334663679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.605 Γ— 10⁹⁷(98-digit number)
16056646466606517899…05809856980669327359
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,610,771 XPMΒ·at block #6,795,835 Β· updates every 60s
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