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Block #693,989

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/26/2014, 4:16:39 PM Β· Difficulty 10.9567 Β· 6,121,943 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
23a1a68d67b5db6c16e23b7d7f927e3a3a380444d13bf23800d5afcf3c4b58d3
View on Chainz β†—

Height

#693,989

Difficulty

10.956709

Transactions

2

Size

878 B

Version

2

Bits

0af4eada

Nonce

968,341,509

Timestamp

8/26/2014, 4:16:39 PM

Confirmations

6,121,943

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

d99ba867062eba468d7c48e235f68377f97f071f71110603f9dfb4804921fd9b
Transactions (2)
Coinbasefa1104eefad38c…42c6135febe12f
1 in β†’ 1 out8.3300 XPM116 B
ANSXnLY2…Sd25TjkD
7c6c2376149378…9c514962cef964
4 in β†’ 2 out15.0172 XPM672 B
AJjhokhu…9Cjwps9gAQXRxGkC…t4W6npAo
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.

6.712 Γ— 10⁹⁡(96-digit number)
67122984107997280993…11425187051415836159
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
6.712 Γ— 10⁹⁡(96-digit number)
67122984107997280993…11425187051415836159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.342 Γ— 10⁹⁢(97-digit number)
13424596821599456198…22850374102831672319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.684 Γ— 10⁹⁢(97-digit number)
26849193643198912397…45700748205663344639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.369 Γ— 10⁹⁢(97-digit number)
53698387286397824794…91401496411326689279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.073 Γ— 10⁹⁷(98-digit number)
10739677457279564958…82802992822653378559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.147 Γ— 10⁹⁷(98-digit number)
21479354914559129917…65605985645306757119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.295 Γ— 10⁹⁷(98-digit number)
42958709829118259835…31211971290613514239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.591 Γ— 10⁹⁷(98-digit number)
85917419658236519671…62423942581227028479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.718 Γ— 10⁹⁸(99-digit number)
17183483931647303934…24847885162454056959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.436 Γ— 10⁹⁸(99-digit number)
34366967863294607868…49695770324908113919
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:57,771,568 XPMΒ·at block #6,815,931 Β· updates every 60s
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