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Block #1,697,794

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/1/2016, 5:08:01 AM Β· Difficulty 10.6728 Β· 5,141,703 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
0d320850a5d149016e454b8f62cdf31807b2b67f4c62da63907e583e14be8299
View on Chainz β†—

Height

#1,697,794

Difficulty

10.672781

Transactions

2

Size

722 B

Version

2

Bits

0aac3b61

Nonce

588,149,533

Timestamp

8/1/2016, 5:08:01 AM

Confirmations

5,141,703

Mined by

⛏️ P2SHAQuVp9UfsUxgEjokgDSFge195om3dEqmNE

Merkle Root

2c6ba851655f4bb1a20d69cca6f74f70251ba8cf9723ad8c69cac40f435156a7
Transactions (2)
Coinbase44fa26bf8b25a6…53a4c7d2c042ee
1 in β†’ 1 out8.7800 XPM110 B
AQuVp9Uf…m3dEqmNE
79bd02fec8d0d4…9b0acc1c0e07e4
3 in β†’ 2 out0.1080 XPM522 B
AJ7br3g8…vb9iLd1NAbumcqEv…ScNcH1V7
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.

3.703 Γ— 10⁹⁡(96-digit number)
37031342647627321289…42607372330483601919
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
3.703 Γ— 10⁹⁡(96-digit number)
37031342647627321289…42607372330483601919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.406 Γ— 10⁹⁡(96-digit number)
74062685295254642578…85214744660967203839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.481 Γ— 10⁹⁢(97-digit number)
14812537059050928515…70429489321934407679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.962 Γ— 10⁹⁢(97-digit number)
29625074118101857031…40858978643868815359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.925 Γ— 10⁹⁢(97-digit number)
59250148236203714062…81717957287737630719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.185 Γ— 10⁹⁷(98-digit number)
11850029647240742812…63435914575475261439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.370 Γ— 10⁹⁷(98-digit number)
23700059294481485625…26871829150950522879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.740 Γ— 10⁹⁷(98-digit number)
47400118588962971250…53743658301901045759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.480 Γ— 10⁹⁷(98-digit number)
94800237177925942500…07487316603802091519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.896 Γ— 10⁹⁸(99-digit number)
18960047435585188500…14974633207604183039
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:57,960,272 XPMΒ·at block #6,839,496 Β· updates every 60s
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