Block #473,945

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/4/2014, 6:38:53 AM · Difficulty 10.4456 · 6,328,643 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bd9971a02a6b0a85d5985bdd904b7c611838cf8fed7f2f111e6ae845ac6b78b5

View on Chainz ↗

Height

#473,945

Difficulty

10.445591

Transactions

Size

935 B

Version

Bits

0a72123e

Nonce

29,268

Timestamp

4/4/2014, 6:38:53 AM

Confirmations

6,328,643

Mined by

⛏️ Y;AdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

45350a317ca82add320bfbe8028285786e4934f1d49be9838ca782953f523028

Transactions (1)

Coinbase45350a317ca82a…a782953f523028

1 in → 23 out9.1500 XPM845 B

AdFLJFhb…bsaVkAyh AGz9gyZW…bo8NYQpw AMW1p9oT…2TzdaZxH AdoqUYAy…tJ482T9b ATp4jJhs…TbSgR8Qb

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.

9.043 × 10⁹⁵(96-digit number)

90431615609619471710…59626511470405427199

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

9.043 × 10⁹⁵(96-digit number)

90431615609619471710…59626511470405427199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.043 × 10⁹⁵(96-digit number)

90431615609619471710…59626511470405427201

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

1.808 × 10⁹⁶(97-digit number)

18086323121923894342…19253022940810854399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.808 × 10⁹⁶(97-digit number)

18086323121923894342…19253022940810854401

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

3.617 × 10⁹⁶(97-digit number)

36172646243847788684…38506045881621708799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.617 × 10⁹⁶(97-digit number)

36172646243847788684…38506045881621708801

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

7.234 × 10⁹⁶(97-digit number)

72345292487695577368…77012091763243417599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.234 × 10⁹⁶(97-digit number)

72345292487695577368…77012091763243417601

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

1.446 × 10⁹⁷(98-digit number)

14469058497539115473…54024183526486835199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.446 × 10⁹⁷(98-digit number)

14469058497539115473…54024183526486835201

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