Block #6,784,932

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/5/2026, 10:57:25 PM · Difficulty 10.9809 · 222 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

0e9a564e704dc24cb68017f9c0d6f104bc019bbfce57eb12d4a8105ef6ddb5a1

View on Chainz ↗

Height

#6,784,932

Difficulty

10.980854

Transactions

Size

192 B

Version

536870912

Bits

0afb1943

Nonce

177,722,007

Timestamp

4/5/2026, 10:57:25 PM

Confirmations

222

Merkle Root

298166f577f78dc2ae0442225d6b9a904d9a681fa36f3e6a4c67e46458eedaa0

Transactions (1)

Coinbase298166f577f78d…67e46458eedaa0

1 in → 1 out8.1790 XPM101 B

AMrLYUQN…jwjifxiz

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.

4.959 × 10⁹⁷(98-digit number)

49596520482702747990…29877955994347796481

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

4.959 × 10⁹⁷(98-digit number)

49596520482702747990…29877955994347796481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

9.919 × 10⁹⁷(98-digit number)

99193040965405495980…59755911988695592961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.983 × 10⁹⁸(99-digit number)

19838608193081099196…19511823977391185921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

3.967 × 10⁹⁸(99-digit number)

39677216386162198392…39023647954782371841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

7.935 × 10⁹⁸(99-digit number)

79354432772324396784…78047295909564743681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.587 × 10⁹⁹(100-digit number)

15870886554464879356…56094591819129487361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

3.174 × 10⁹⁹(100-digit number)

31741773108929758713…12189183638258974721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

6.348 × 10⁹⁹(100-digit number)

63483546217859517427…24378367276517949441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.269 × 10¹⁰⁰(101-digit number)

12696709243571903485…48756734553035898881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

2.539 × 10¹⁰⁰(101-digit number)

25393418487143806970…97513469106071797761

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 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

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 2CC formula:

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

Cross-reference on Chainz Explorer