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Block #666,760

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/7/2014, 6:15:44 AM Β· Difficulty 10.9617 Β· 6,143,446 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b86e3d35f56afa59a56a9d941d9242792e786dc556ae6129d6beeaf49dd6de1b
View on Chainz β†—

Height

#666,760

Difficulty

10.961706

Transactions

2

Size

1.29 KB

Version

2

Bits

0af6325c

Nonce

1,112,167,483

Timestamp

8/7/2014, 6:15:44 AM

Confirmations

6,143,446

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

61c6130bf46966411f485435dcbdf25569236b34cec34bff6ac7c41dd6e71dc3
Transactions (2)
Coinbase604bf0db599619…c331fd6b5c8d94
1 in β†’ 1 out8.3300 XPM116 B
ANSXnLY2…Sd25TjkD
fc3e583904659c…ad37471dfb3f3f
7 in β†’ 2 out608.9007 XPM1.09 KB
AYGMmGyW…7KB9f22HASr3bZTk…N5Tt9pWP
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.

7.499 Γ— 10⁹⁢(97-digit number)
74997432225728426691…93407221117606195199
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
7.499 Γ— 10⁹⁢(97-digit number)
74997432225728426691…93407221117606195199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.499 Γ— 10⁹⁷(98-digit number)
14999486445145685338…86814442235212390399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.999 Γ— 10⁹⁷(98-digit number)
29998972890291370676…73628884470424780799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.999 Γ— 10⁹⁷(98-digit number)
59997945780582741353…47257768940849561599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.199 Γ— 10⁹⁸(99-digit number)
11999589156116548270…94515537881699123199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.399 Γ— 10⁹⁸(99-digit number)
23999178312233096541…89031075763398246399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.799 Γ— 10⁹⁸(99-digit number)
47998356624466193082…78062151526796492799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.599 Γ— 10⁹⁸(99-digit number)
95996713248932386165…56124303053592985599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.919 Γ— 10⁹⁹(100-digit number)
19199342649786477233…12248606107185971199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.839 Γ— 10⁹⁹(100-digit number)
38398685299572954466…24497212214371942399
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:57,725,721 XPMΒ·at block #6,810,205 Β· updates every 60s
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