Block #513,554

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/27/2014, 2:34:39 PM · Difficulty 10.8357 · 6,296,941 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b34d49d133e59b3d3409caa93e53a038a6d13d563726f9f0b3b625ae7116264c

View on Chainz ↗

Height

#513,554

Difficulty

10.835714

Transactions

Size

771 B

Version

Bits

0ad5f15f

Nonce

9,476

Timestamp

4/27/2014, 2:34:39 PM

Confirmations

6,296,941

Mined by

⛏️ fyAREQGaCCeRHuaNkf53p3iT4PbrV47D9Shh

Merkle Root

6cb90f74b0e08f236fbf1157f26f481ddb9da030fb26ea22107e2d682b43b1df

Transactions (1)

Coinbase6cb90f74b0e08f…7e2d682b43b1df

1 in → 18 out8.5000 XPM675 B

AREQGaCC…V47D9Shh AMVf7Jrg…xd5AVR7C AGz9gyZW…bo8NYQpw 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.

2.205 × 10¹¹⁰(111-digit number)

22059247736924179452…32779854907098191579

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

2.205 × 10¹¹⁰(111-digit number)

22059247736924179452…32779854907098191579

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.205 × 10¹¹⁰(111-digit number)

22059247736924179452…32779854907098191581

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

4.411 × 10¹¹⁰(111-digit number)

44118495473848358904…65559709814196383159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.411 × 10¹¹⁰(111-digit number)

44118495473848358904…65559709814196383161

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

8.823 × 10¹¹⁰(111-digit number)

88236990947696717808…31119419628392766319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.823 × 10¹¹⁰(111-digit number)

88236990947696717808…31119419628392766321

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

1.764 × 10¹¹¹(112-digit number)

17647398189539343561…62238839256785532639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.764 × 10¹¹¹(112-digit number)

17647398189539343561…62238839256785532641

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

3.529 × 10¹¹¹(112-digit number)

35294796379078687123…24477678513571065279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.529 × 10¹¹¹(112-digit number)

35294796379078687123…24477678513571065281

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 #513,554

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