Block #2,017,702

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/11/2017, 1:00:54 AM · Difficulty 10.7162 · 4,779,199 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

46121ccf26df8fb00e91bee535057d358d08c029c496dd0e4f95e229a1455461

View on Chainz ↗

Height

#2,017,702

Difficulty

10.716211

Transactions

Size

238 B

Version

Bits

0ab759a3

Nonce

14,990

Timestamp

3/11/2017, 1:00:54 AM

Confirmations

4,779,199

Mined by

⛏️ P2SHAJCcxnuA2gFsc6HJAVptkiMzbSBeS8SCFB

Merkle Root

092ece81e9d6fdf76077f316fe507e7f754f180cb00462eb6299dff0a89ac621

Transactions (1)

Coinbase092ece81e9d6fd…99dff0a89ac621

1 in → 2 out8.6900 XPM146 B

AJCcxnuA…BeS8SCFB Ac7DbgrK…XDMazkvn

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

6.166 × 10⁹⁹(100-digit number)

61664508116863601853…20212742491760506079

Discovered Prime Numbers

p_k = 2^k × origin − 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.

origin − 1

6.166 × 10⁹⁹(100-digit number)

61664508116863601853…20212742491760506079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.233 × 10¹⁰⁰(101-digit number)

12332901623372720370…40425484983521012159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.466 × 10¹⁰⁰(101-digit number)

24665803246745440741…80850969967042024319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

4.933 × 10¹⁰⁰(101-digit number)

49331606493490881483…61701939934084048639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

9.866 × 10¹⁰⁰(101-digit number)

98663212986981762966…23403879868168097279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.973 × 10¹⁰¹(102-digit number)

19732642597396352593…46807759736336194559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

3.946 × 10¹⁰¹(102-digit number)

39465285194792705186…93615519472672389119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

7.893 × 10¹⁰¹(102-digit number)

78930570389585410372…87231038945344778239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.578 × 10¹⁰²(103-digit number)

15786114077917082074…74462077890689556479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

3.157 × 10¹⁰²(103-digit number)

31572228155834164149…48924155781379112959

Verify on FactorDB ↗Wolfram Alpha ↗

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 — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆

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 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …

Cross-reference on Chainz Explorer