Block #6,784,929

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 4/5/2026, 10:54:35 PM · Difficulty 10.9809 · 225 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

b8f829b423861240051ead844adbda887dd006b77ee016b9304662979da325fb

View on Chainz ↗

Height

#6,784,929

Difficulty

10.980856

Transactions

Size

191 B

Version

536870912

Bits

0afb195b

Nonce

135,551,206

Timestamp

4/5/2026, 10:54:35 PM

Confirmations

225

Merkle Root

ed3f4c5fe007fcd30fb283d7974dfc20933a05df8831666b03cd934477cf24d1

Transactions (1)

Coinbaseed3f4c5fe007fc…cd934477cf24d1

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.

1.069 × 10⁹⁴(95-digit number)

10691832238888426182…40033115918578286001

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

1.069 × 10⁹⁴(95-digit number)

10691832238888426182…40033115918578286001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.138 × 10⁹⁴(95-digit number)

21383664477776852364…80066231837156572001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

4.276 × 10⁹⁴(95-digit number)

42767328955553704728…60132463674313144001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

8.553 × 10⁹⁴(95-digit number)

85534657911107409457…20264927348626288001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.710 × 10⁹⁵(96-digit number)

17106931582221481891…40529854697252576001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

3.421 × 10⁹⁵(96-digit number)

34213863164442963782…81059709394505152001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

6.842 × 10⁹⁵(96-digit number)

68427726328885927565…62119418789010304001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.368 × 10⁹⁶(97-digit number)

13685545265777185513…24238837578020608001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.737 × 10⁹⁶(97-digit number)

27371090531554371026…48477675156041216001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

5.474 × 10⁹⁶(97-digit number)

54742181063108742052…96955350312082432001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^10 × origin + 1

1.094 × 10⁹⁷(98-digit number)

10948436212621748410…93910700624164864001

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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