Block #248,083

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/7/2013, 4:13:23 AM · Difficulty 9.9654 · 6,542,911 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

ad03764a2c27626ec47a9c89fc776ddd1a7f0e01aaad8e34debfe99795102708

View on Chainz ↗

Height

#248,083

Difficulty

9.965409

Transactions

Size

653 B

Version

Bits

09f7250b

Nonce

58,249

Timestamp

11/7/2013, 4:13:23 AM

Confirmations

6,542,911

Merkle Root

781a313990e584f121b277e38181483de4b5dddda8303f090a0e653e48fea7f6

Transactions (3)

Coinbase28af79fa03c015…23fa5e150634f6

1 in → 1 out10.0700 XPM109 B

AXzWVUGo…qCPXptD4

b45bfa6f7cc884…fdbf6dcc3b1fad

1 in → 2 out10.0500 XPM227 B

Af1pWfN1…XP3hbDrt AdVoMqmQ…eZmBx2Br

2681b07cd3eb03…b1a90c3404d59f

1 in → 2 out6.0280 XPM225 B

ASnSjgQg…fewAaNPL ARqRo495…yGBvF9jt

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.

2.472 × 10¹⁰⁰(101-digit number)

24725990828606603835…18071010718684774401

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

2.472 × 10¹⁰⁰(101-digit number)

24725990828606603835…18071010718684774401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

4.945 × 10¹⁰⁰(101-digit number)

49451981657213207671…36142021437369548801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

9.890 × 10¹⁰⁰(101-digit number)

98903963314426415343…72284042874739097601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.978 × 10¹⁰¹(102-digit number)

19780792662885283068…44568085749478195201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

3.956 × 10¹⁰¹(102-digit number)

39561585325770566137…89136171498956390401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

7.912 × 10¹⁰¹(102-digit number)

79123170651541132274…78272342997912780801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.582 × 10¹⁰²(103-digit number)

15824634130308226454…56544685995825561601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

3.164 × 10¹⁰²(103-digit number)

31649268260616452909…13089371991651123201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

6.329 × 10¹⁰²(103-digit number)

63298536521232905819…26178743983302246401

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 consecutive prime numbers forming a Cunningham Chain of the Second 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 2CC formula:

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

Cross-reference on Chainz Explorer