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Block #664,988

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/6/2014, 5:41:48 AM Β· Difficulty 10.9593 Β· 6,143,033 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
714950f0658fc43ea33d3d2ccac03111aec1e29fa438c840d9447a75302f9eaa
View on Chainz β†—

Height

#664,988

Difficulty

10.959318

Transactions

2

Size

432 B

Version

2

Bits

0af595e1

Nonce

840,227,894

Timestamp

8/6/2014, 5:41:48 AM

Confirmations

6,143,033

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

1ddf856b98801af4c170d36063098611a34b10b4686af06b99c9308fdfa82526
Transactions (2)
Coinbase6711c674bc71b3…76e0384a3e4f83
1 in β†’ 1 out8.3200 XPM116 B
ANSXnLY2…Sd25TjkD
79b739b72b5f51…9946d0e567e0b3
1 in β†’ 2 out548.9721 XPM225 B
ANciy2Lw…zTXo6EFaALtsYLdB…g7K71kH3
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.

3.423 Γ— 10⁹⁢(97-digit number)
34234299346508871937…87260631700290104959
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
3.423 Γ— 10⁹⁢(97-digit number)
34234299346508871937…87260631700290104959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.846 Γ— 10⁹⁢(97-digit number)
68468598693017743874…74521263400580209919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.369 Γ— 10⁹⁷(98-digit number)
13693719738603548774…49042526801160419839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.738 Γ— 10⁹⁷(98-digit number)
27387439477207097549…98085053602320839679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.477 Γ— 10⁹⁷(98-digit number)
54774878954414195099…96170107204641679359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.095 Γ— 10⁹⁸(99-digit number)
10954975790882839019…92340214409283358719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.190 Γ— 10⁹⁸(99-digit number)
21909951581765678039…84680428818566717439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.381 Γ— 10⁹⁸(99-digit number)
43819903163531356079…69360857637133434879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.763 Γ— 10⁹⁸(99-digit number)
87639806327062712159…38721715274266869759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.752 Γ— 10⁹⁹(100-digit number)
17527961265412542431…77443430548533739519
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:57,708,211 XPMΒ·at block #6,808,020 Β· updates every 60s
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