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Block #672,067

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/10/2014, 4:46:55 PM Β· Difficulty 10.9645 Β· 6,160,916 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
69418ced8af6a414e5462e7676404539913ffb6ef10c969cef069c7c572adf28
View on Chainz β†—

Height

#672,067

Difficulty

10.964474

Transactions

1

Size

206 B

Version

2

Bits

0af6e7c4

Nonce

542,257,784

Timestamp

8/10/2014, 4:46:55 PM

Confirmations

6,160,916

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

3a48720f5120214eb5e21ce7303662a767cd6a51e5b083becdd8e18f548aa49d
Transactions (1)
Coinbase3a48720f512021…d8e18f548aa49d
1 in β†’ 1 out8.3000 XPM116 B
ANSXnLY2…Sd25TjkD
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.

4.758 Γ— 10⁹³(94-digit number)
47581065972965062771…64101116701153218259
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
4.758 Γ— 10⁹³(94-digit number)
47581065972965062771…64101116701153218259
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
9.516 Γ— 10⁹³(94-digit number)
95162131945930125543…28202233402306436519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.903 Γ— 10⁹⁴(95-digit number)
19032426389186025108…56404466804612873039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.806 Γ— 10⁹⁴(95-digit number)
38064852778372050217…12808933609225746079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.612 Γ— 10⁹⁴(95-digit number)
76129705556744100434…25617867218451492159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.522 Γ— 10⁹⁡(96-digit number)
15225941111348820086…51235734436902984319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.045 Γ— 10⁹⁡(96-digit number)
30451882222697640173…02471468873805968639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.090 Γ— 10⁹⁡(96-digit number)
60903764445395280347…04942937747611937279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.218 Γ— 10⁹⁢(97-digit number)
12180752889079056069…09885875495223874559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.436 Γ— 10⁹⁢(97-digit number)
24361505778158112139…19771750990447749119
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:57,908,033 XPMΒ·at block #6,832,982 Β· updates every 60s
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