Block #513,546

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/27/2014, 2:26:10 PM · Difficulty 10.8357 · 6,313,750 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9687421f0346b7dd133bcac5dc967ef0d302a91d8b885be3db2db36d53211393

View on Chainz ↗

Height

#513,546

Difficulty

10.835696

Transactions

Size

800 B

Version

Bits

0ad5f030

Nonce

211,618,321

Timestamp

4/27/2014, 2:26:10 PM

Confirmations

6,313,750

Mined by

⛏️ e$AREQGaCCeRHuaNkf53p3iT4PbrV47D9Shh

Merkle Root

2712cf9f63501a13806b1a695922b7963d45b4a131b9c81a1d59b1eaa0a6b40c

Transactions (1)

Coinbase2712cf9f63501a…59b1eaa0a6b40c

1 in → 19 out8.5000 XPM709 B

AREQGaCC…V47D9Shh AGz9gyZW…bo8NYQpw AMVf7Jrg…xd5AVR7C AH5mD99t…Spv1yg4N 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.

1.799 × 10⁹⁷(98-digit number)

17997048587321588418…48566472342734318879

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

1.799 × 10⁹⁷(98-digit number)

17997048587321588418…48566472342734318879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.799 × 10⁹⁷(98-digit number)

17997048587321588418…48566472342734318881

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

3.599 × 10⁹⁷(98-digit number)

35994097174643176837…97132944685468637759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.599 × 10⁹⁷(98-digit number)

35994097174643176837…97132944685468637761

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

7.198 × 10⁹⁷(98-digit number)

71988194349286353675…94265889370937275519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.198 × 10⁹⁷(98-digit number)

71988194349286353675…94265889370937275521

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

1.439 × 10⁹⁸(99-digit number)

14397638869857270735…88531778741874551039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.439 × 10⁹⁸(99-digit number)

14397638869857270735…88531778741874551041

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

2.879 × 10⁹⁸(99-digit number)

28795277739714541470…77063557483749102079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.879 × 10⁹⁸(99-digit number)

28795277739714541470…77063557483749102081

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 #513,546

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