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Block #288,376

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/1/2013, 5:25:33 PM Β· Difficulty 9.9876 Β· 6,554,620 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
48f3a8fd1b745060d82810654d12cc0bf9c239baae925ed8e398614ff741cecf
View on Chainz β†—

Height

#288,376

Difficulty

9.987642

Transactions

1

Size

206 B

Version

2

Bits

09fcd61a

Nonce

176,147

Timestamp

12/1/2013, 5:25:33 PM

Confirmations

6,554,620

Mined by

⛏️ P2SHAcLBm5Z9BD7o7btAchFh9KZEkSS683d7c3

Merkle Root

eade45ad4fbf57c68830d3b206f3398ff3cb3a28fb2028a68a139d0630e1dabd
Transactions (1)
Coinbaseeade45ad4fbf57…139d0630e1dabd
1 in β†’ 1 out10.0100 XPM116 B
AcLBm5Z9…S683d7c3
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.

2.396 Γ— 10⁹⁴(95-digit number)
23964199407558190964…83659704886333199159
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
2.396 Γ— 10⁹⁴(95-digit number)
23964199407558190964…83659704886333199159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.792 Γ— 10⁹⁴(95-digit number)
47928398815116381928…67319409772666398319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.585 Γ— 10⁹⁴(95-digit number)
95856797630232763857…34638819545332796639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.917 Γ— 10⁹⁡(96-digit number)
19171359526046552771…69277639090665593279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.834 Γ— 10⁹⁡(96-digit number)
38342719052093105543…38555278181331186559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.668 Γ— 10⁹⁡(96-digit number)
76685438104186211086…77110556362662373119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.533 Γ— 10⁹⁢(97-digit number)
15337087620837242217…54221112725324746239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.067 Γ— 10⁹⁢(97-digit number)
30674175241674484434…08442225450649492479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.134 Γ— 10⁹⁢(97-digit number)
61348350483348968868…16884450901298984959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.226 Γ— 10⁹⁷(98-digit number)
12269670096669793773…33768901802597969919
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:57,988,323 XPMΒ·at block #6,842,995 Β· updates every 60s
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