Block #6,784,934

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/5/2026, 10:59:04 PM · Difficulty 10.9809 · 220 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

1b453f408ca09f5d545b29dcbf20cad4b7d7a235c786061f7e8239436ab1720c

View on Chainz ↗

Height

#6,784,934

Difficulty

10.980858

Transactions

Size

191 B

Version

536870912

Bits

0afb198a

Nonce

472,329,127

Timestamp

4/5/2026, 10:59:04 PM

Confirmations

220

Merkle Root

9d470e6ee70c2d59100ef1c5db53c2ea43800816c353ff0d985ae4b468177ae6

Transactions (1)

Coinbase9d470e6ee70c2d…5ae4b468177ae6

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.

1.525 × 10⁹⁴(95-digit number)

15259943247369778067…02434143827435811839

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 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.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

1.525 × 10⁹⁴(95-digit number)

15259943247369778067…02434143827435811839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.525 × 10⁹⁴(95-digit number)

15259943247369778067…02434143827435811841

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

3.051 × 10⁹⁴(95-digit number)

30519886494739556134…04868287654871623679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.051 × 10⁹⁴(95-digit number)

30519886494739556134…04868287654871623681

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

6.103 × 10⁹⁴(95-digit number)

61039772989479112268…09736575309743247359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.103 × 10⁹⁴(95-digit number)

61039772989479112268…09736575309743247361

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

1.220 × 10⁹⁵(96-digit number)

12207954597895822453…19473150619486494719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.220 × 10⁹⁵(96-digit number)

12207954597895822453…19473150619486494721

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

2.441 × 10⁹⁵(96-digit number)

24415909195791644907…38946301238972989439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.441 × 10⁹⁵(96-digit number)

24415909195791644907…38946301238972989441

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

4.883 × 10⁹⁵(96-digit number)

48831818391583289814…77892602477945978879

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 Bi-Twin Chain. 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 TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer