Block #513,399

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/27/2014, 12:18:30 PM · Difficulty 10.8351 · 6,313,758 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

33ea869d2d25a1308f7c997b0795373265927cac3c861932052d380e99330648

View on Chainz ↗

Height

#513,399

Difficulty

10.835080

Transactions

Size

1.36 KB

Version

Bits

0ad5c7cd

Nonce

267,175,866

Timestamp

4/27/2014, 12:18:30 PM

Confirmations

6,313,758

Mined by

⛏️ P2SHAS5bLmAstGJK9XyWuwFrFauy2R3p5Kmfv4

Merkle Root

97682c69cbe33545c8be33b6cdc337f55da83dde6331806b6ab69be48cd89df1

Transactions (3)

Coinbaseb84efbc169272c…8bd086c8c9ec31

1 in → 1 out8.5200 XPM110 B

AS5bLmAs…3p5Kmfv4

5a32aa73e16456…e0f7b9c81f1d68

6 in → 2 out12.8164 XPM968 B

AVcbRNgz…rXA3MCRb AeViZaDT…hdPZPm53

01f5d814a2b1f9…fe38d0af731566

1 in → 2 out2.3988 XPM226 B

Ad8CYYJn…vYFaCwUP AGXqJki6…YNiMZGMN

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.

1.726 × 10⁹⁸(99-digit number)

17263063953027472090…82827403923406436799

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

1.726 × 10⁹⁸(99-digit number)

17263063953027472090…82827403923406436799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.726 × 10⁹⁸(99-digit number)

17263063953027472090…82827403923406436801

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

3.452 × 10⁹⁸(99-digit number)

34526127906054944180…65654807846812873599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.452 × 10⁹⁸(99-digit number)

34526127906054944180…65654807846812873601

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

6.905 × 10⁹⁸(99-digit number)

69052255812109888360…31309615693625747199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.905 × 10⁹⁸(99-digit number)

69052255812109888360…31309615693625747201

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

1.381 × 10⁹⁹(100-digit number)

13810451162421977672…62619231387251494399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.381 × 10⁹⁹(100-digit number)

13810451162421977672…62619231387251494401

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

2.762 × 10⁹⁹(100-digit number)

27620902324843955344…25238462774502988799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.762 × 10⁹⁹(100-digit number)

27620902324843955344…25238462774502988801

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 #513,399

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