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Block #152,457

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/6/2013, 8:30:04 AM Β· Difficulty 9.8623 Β· 6,655,727 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
6b090d160b61ba79c54a203af5c5111c5473259a85bd5882cffb0b7ee2cd1e2d
View on Chainz β†—

Height

#152,457

Difficulty

9.862318

Transactions

2

Size

391 B

Version

2

Bits

09dcc0e0

Nonce

10,397

Timestamp

9/6/2013, 8:30:04 AM

Confirmations

6,655,727

Mined by

⛏️ P2SHAQGz9h1x7euuJVUVqRVhcyEPS83RpsqhCW

Merkle Root

13c903b9a527fc785a8b3fc915cbb790bca8c7f6bafe02bd68ad9185296bbdd4
Transactions (2)
Coinbase0b68d62b0c7da7…ba6a5fc931693a
1 in β†’ 1 out10.2800 XPM109 B
AQGz9h1x…3RpsqhCW
5d3afeadc70e8d…61d57a1c472b42
1 in β†’ 2 out10.3000 XPM192 B
AFz9fXym…wh4UqpkLAaNGP3TN…KJwMJvCN
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.

5.228 Γ— 10⁹³(94-digit number)
52289288487637152914…43633386174351792319
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
5.228 Γ— 10⁹³(94-digit number)
52289288487637152914…43633386174351792319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.045 Γ— 10⁹⁴(95-digit number)
10457857697527430582…87266772348703584639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.091 Γ— 10⁹⁴(95-digit number)
20915715395054861165…74533544697407169279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.183 Γ— 10⁹⁴(95-digit number)
41831430790109722331…49067089394814338559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.366 Γ— 10⁹⁴(95-digit number)
83662861580219444663…98134178789628677119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.673 Γ— 10⁹⁡(96-digit number)
16732572316043888932…96268357579257354239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.346 Γ— 10⁹⁡(96-digit number)
33465144632087777865…92536715158514708479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.693 Γ— 10⁹⁡(96-digit number)
66930289264175555730…85073430317029416959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.338 Γ— 10⁹⁢(97-digit number)
13386057852835111146…70146860634058833919
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,709,521 XPMΒ·at block #6,808,183 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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