Block #98,481

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 8/5/2013, 6:16:20 AM · Difficulty 9.3462 · 6,698,029 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

6b9ee492c72ba8592fd2dc7e4bf031083b7c2e9bffac0642d5276492e0b07c62

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Height

#98,481

Difficulty

9.346246

Transactions

Size

207 B

Version

Bits

0958a39a

Nonce

67,778

Timestamp

8/5/2013, 6:16:20 AM

Confirmations

6,698,029

Mined by

⛏️ P2SHAHttmdT5YuWLkWWUyh67xAHHzFt6ixRPND

Merkle Root

8abc8b501337774796915babcdb82b90acba2211faba8356e199764dcfe8b2a1

Transactions (1)

Coinbase8abc8b50133777…99764dcfe8b2a1

1 in → 1 out11.4300 XPM109 B

AHttmdT5…t6ixRPND

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.

9.802 × 10¹¹²(113-digit number)

98028799336550706748…39529821720851573851

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

9.802 × 10¹¹²(113-digit number)

98028799336550706748…39529821720851573851

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.960 × 10¹¹³(114-digit number)

19605759867310141349…79059643441703147701

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

3.921 × 10¹¹³(114-digit number)

39211519734620282699…58119286883406295401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

7.842 × 10¹¹³(114-digit number)

78423039469240565398…16238573766812590801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.568 × 10¹¹⁴(115-digit number)

15684607893848113079…32477147533625181601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

3.136 × 10¹¹⁴(115-digit number)

31369215787696226159…64954295067250363201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

6.273 × 10¹¹⁴(115-digit number)

62738431575392452319…29908590134500726401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.254 × 10¹¹⁵(116-digit number)

12547686315078490463…59817180269001452801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.509 × 10¹¹⁵(116-digit number)

25095372630156980927…19634360538002905601

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