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Block #339,972

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/2/2014, 11:42:25 AM Β· Difficulty 10.1274 Β· 6,472,832 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b300c72a7df1a75c1f9b21cf4aba216cefac5e16e22d1644d78e596c059dc29e
View on Chainz β†—

Height

#339,972

Difficulty

10.127359

Transactions

1

Size

206 B

Version

2

Bits

0a209aa0

Nonce

469,763,688

Timestamp

1/2/2014, 11:42:25 AM

Confirmations

6,472,832

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

612ac5769fe52d229917046d3036cd7ecef828798fa0e189b7768d42c4c4ee5b
Transactions (1)
Coinbase612ac5769fe52d…768d42c4c4ee5b
1 in β†’ 1 out9.7400 XPM116 B
AbwWkWZt…kawDhufa
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.

5.399 Γ— 10⁹⁡(96-digit number)
53995907605981040594…83719954422382694159
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
5.399 Γ— 10⁹⁡(96-digit number)
53995907605981040594…83719954422382694159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.079 Γ— 10⁹⁢(97-digit number)
10799181521196208118…67439908844765388319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.159 Γ— 10⁹⁢(97-digit number)
21598363042392416237…34879817689530776639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.319 Γ— 10⁹⁢(97-digit number)
43196726084784832475…69759635379061553279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.639 Γ— 10⁹⁢(97-digit number)
86393452169569664951…39519270758123106559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.727 Γ— 10⁹⁷(98-digit number)
17278690433913932990…79038541516246213119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.455 Γ— 10⁹⁷(98-digit number)
34557380867827865980…58077083032492426239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.911 Γ— 10⁹⁷(98-digit number)
69114761735655731961…16154166064984852479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.382 Γ— 10⁹⁸(99-digit number)
13822952347131146392…32308332129969704959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.764 Γ— 10⁹⁸(99-digit number)
27645904694262292784…64616664259939409919
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:57,746,476 XPMΒ·at block #6,812,803 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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