Block #457,377

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/23/2014, 8:49:01 PM · Difficulty 10.4202 · 6,337,476 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

275cb5390c24230de068be794c832cfdbeb87a70b0efd4a4432d710fd1eecc28

View on Chainz ↗

Height

#457,377

Difficulty

10.420180

Transactions

Size

2.06 KB

Version

Bits

0a6b90e5

Nonce

49,258

Timestamp

3/23/2014, 8:49:01 PM

Confirmations

6,337,476

Mined by

AdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

b653701fcd5470f3d6946de5cc9d5808496621cc96d2e4e98bd2c9299efaf9fe

Transactions (2)

Coinbasef536c86f753a37…272c31c02d41cb

1 in → 25 out9.2200 XPM913 B

AdFLJFhb…bsaVkAyh AH5mD99t…Spv1yg4N AGz9gyZW…bo8NYQpw ATgnfdX6…cHVEZtsd AbHY4iza…Yckt2J5W

a03ff7aed45090…91180361d3023f

6 in → 6 out8.0147 XPM1.08 KB

AG9SfhhW…sSJdWcrQ AVHcc9zb…JkngbvXL AJ6Fiu6B…tbWLzJrw AHbGXzeD…A3SKohbN AVg5YGji…Aq7MMxRC

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.

2.156 × 10⁹⁶(97-digit number)

21567640120095653194…31302549415291994899

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

2.156 × 10⁹⁶(97-digit number)

21567640120095653194…31302549415291994899

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.156 × 10⁹⁶(97-digit number)

21567640120095653194…31302549415291994901

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

4.313 × 10⁹⁶(97-digit number)

43135280240191306388…62605098830583989799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.313 × 10⁹⁶(97-digit number)

43135280240191306388…62605098830583989801

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

8.627 × 10⁹⁶(97-digit number)

86270560480382612776…25210197661167979599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.627 × 10⁹⁶(97-digit number)

86270560480382612776…25210197661167979601

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

1.725 × 10⁹⁷(98-digit number)

17254112096076522555…50420395322335959199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.725 × 10⁹⁷(98-digit number)

17254112096076522555…50420395322335959201

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

3.450 × 10⁹⁷(98-digit number)

34508224192153045110…00840790644671918399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.450 × 10⁹⁷(98-digit number)

34508224192153045110…00840790644671918401

Verify on FactorDB ↗Wolfram Alpha ↗

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

What this block proved

The miner who found this block proved the existence of 10 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

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 TWN formula:

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

Cross-reference on Chainz Explorer