Block #1,501,994

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/18/2016, 11:08:12 AM · Difficulty 10.6426 · 5,329,190 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e04357e3b1141ff01586393c0d3f7f1a01d4e990314f25708cb104212650d11d

View on Chainz ↗

Height

#1,501,994

Difficulty

10.642635

Transactions

Size

1.11 KB

Version

Bits

0aa483b4

Nonce

962,059,880

Timestamp

3/18/2016, 11:08:12 AM

Confirmations

5,329,190

Mined by

⛏️ P2SHAV52zG9pbEBktiWp1Lk14aQ8qBZ1SwyCnV

Merkle Root

0deebb6bc5a6107c7e32a609c7f6ea499b5606b062eafec8e2407f8e258bb8df

Transactions (2)

Coinbase844f6663c97dbd…240e770747cb5f

1 in → 1 out8.8200 XPM109 B

AV52zG9p…Z1SwyCnV

c5c0cf98305a53…9e159e2d71a092

1 in → 23 out34.2498 XPM940 B

AVTAhGc5…vxRKFsZp AdaBtph9…HrUiucBr AZGu2LFf…R1xomEtn Acpy9Hyf…3VgvNDkf ANeyCe88…Np4Tmudi

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.

2.447 × 10⁹⁷(98-digit number)

24479169046317225736…13491004412797276159

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

2.447 × 10⁹⁷(98-digit number)

24479169046317225736…13491004412797276159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.447 × 10⁹⁷(98-digit number)

24479169046317225736…13491004412797276161

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

4.895 × 10⁹⁷(98-digit number)

48958338092634451473…26982008825594552319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.895 × 10⁹⁷(98-digit number)

48958338092634451473…26982008825594552321

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

9.791 × 10⁹⁷(98-digit number)

97916676185268902946…53964017651189104639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.791 × 10⁹⁷(98-digit number)

97916676185268902946…53964017651189104641

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

1.958 × 10⁹⁸(99-digit number)

19583335237053780589…07928035302378209279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.958 × 10⁹⁸(99-digit number)

19583335237053780589…07928035302378209281

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

3.916 × 10⁹⁸(99-digit number)

39166670474107561178…15856070604756418559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.916 × 10⁹⁸(99-digit number)

39166670474107561178…15856070604756418561

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 #1,501,994

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