Block #1,494,572

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/13/2016, 3:07:52 AM · Difficulty 10.6600 · 5,331,122 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bd729c7d1ffe50bd57b2802f0fa5878fe729455e6c477405c67b9e3d3e2886ca

View on Chainz ↗

Height

#1,494,572

Difficulty

10.660012

Transactions

Size

766 B

Version

Bits

0aa8f685

Nonce

615,989,809

Timestamp

3/13/2016, 3:07:52 AM

Confirmations

5,331,122

Mined by

⛏️ P2SHAKcbGis63cP8ZMwWE1hHm2kVxQjsgWct92

Merkle Root

d8d9ccde536c95e0f32c9f59d3ea07bf0164da7b34b9f505c4b8437aeb013cfc

Transactions (2)

Coinbase84aa1085703eb3…252aea64eed320

1 in → 1 out8.8000 XPM109 B

AKcbGis6…jsgWct92

8b9be1ace92771…302303039a19d1

1 in → 12 out149.6785 XPM567 B

Ae9TMTyW…isnN4Z2G AVA234pf…hfXcvGVm AdzvYMJi…DDea9q7x ATZuEKEX…qjL4mRxL ATH1rk2S…2U19MGCE

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.

1.897 × 10⁹⁴(95-digit number)

18978318436488289856…93447115106467923559

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

1.897 × 10⁹⁴(95-digit number)

18978318436488289856…93447115106467923559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.897 × 10⁹⁴(95-digit number)

18978318436488289856…93447115106467923561

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

3.795 × 10⁹⁴(95-digit number)

37956636872976579712…86894230212935847119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.795 × 10⁹⁴(95-digit number)

37956636872976579712…86894230212935847121

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

7.591 × 10⁹⁴(95-digit number)

75913273745953159424…73788460425871694239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.591 × 10⁹⁴(95-digit number)

75913273745953159424…73788460425871694241

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

1.518 × 10⁹⁵(96-digit number)

15182654749190631884…47576920851743388479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.518 × 10⁹⁵(96-digit number)

15182654749190631884…47576920851743388481

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

3.036 × 10⁹⁵(96-digit number)

30365309498381263769…95153841703486776959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.036 × 10⁹⁵(96-digit number)

30365309498381263769…95153841703486776961

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

Block #1,494,572

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