Block #515,586

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/28/2014, 9:21:04 PM · Difficulty 10.8418 · 6,294,920 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

596e089709a255fa522d1113fceaa97b1fe6c7d3e5056892b4636a9518d872c1

View on Chainz ↗

Height

#515,586

Difficulty

10.841803

Transactions

Size

1.08 KB

Version

Bits

0ad78066

Nonce

198,950,186

Timestamp

4/28/2014, 9:21:04 PM

Confirmations

6,294,920

Mined by

⛏️ P2SHAZYQixsx2U6yEYic73eWKU4qy89p94sDMF

Merkle Root

5ad63fffd0592311c2dc4a2b1acacd16f11ae832c36370eea1a6897ec3ad7ae1

Transactions (5)

Coinbase1baa5a1a99590a…b1df38e27ea0d0

1 in → 1 out8.5300 XPM109 B

AZYQixsx…9p94sDMF

6bed6d04c74161…b533d4782a2da1

1 in → 2 out6.2583 XPM225 B

AHt2xB4g…TLho1X8P AaYHqHri…NkJoi7nG

f3dce6fc6bdf3e…a1acf07dc54617

1 in → 2 out5.8946 XPM226 B

AdfAtr3G…dcWu6fUn AXnL68UR…jsxeGUhN

f23e7ef03be72f…20c38490804a82

1 in → 2 out5.0651 XPM227 B

AM4PFgce…7dKaKg6Z AaMzeSov…6DUMG3Sc

e881c5c678e2a0…104db417a810df

1 in → 2 out1.1196 XPM227 B

AG8u7ddV…cU5QJSqk AVYvKWEM…BZX4iaR9

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.

3.851 × 10⁹⁰(91-digit number)

38518728026888868673…87446616084357581299

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

3.851 × 10⁹⁰(91-digit number)

38518728026888868673…87446616084357581299

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.851 × 10⁹⁰(91-digit number)

38518728026888868673…87446616084357581301

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

7.703 × 10⁹⁰(91-digit number)

77037456053777737346…74893232168715162599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.703 × 10⁹⁰(91-digit number)

77037456053777737346…74893232168715162601

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

1.540 × 10⁹¹(92-digit number)

15407491210755547469…49786464337430325199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.540 × 10⁹¹(92-digit number)

15407491210755547469…49786464337430325201

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

3.081 × 10⁹¹(92-digit number)

30814982421511094938…99572928674860650399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.081 × 10⁹¹(92-digit number)

30814982421511094938…99572928674860650401

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

6.162 × 10⁹¹(92-digit number)

61629964843022189877…99145857349721300799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.162 × 10⁹¹(92-digit number)

61629964843022189877…99145857349721300801

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.232 × 10⁹²(93-digit number)

12325992968604437975…98291714699442601599

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #515,586

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