Block #516,955

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/29/2014, 3:53:55 PM · Difficulty 10.8497 · 6,291,803 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ecafa54ad06ba2f2fec8b9df9cd059f89342007cf901c3ee1043f996d770ee36

View on Chainz ↗

Height

#516,955

Difficulty

10.849690

Transactions

Size

1.23 KB

Version

Bits

0ad9854f

Nonce

70,440,506

Timestamp

4/29/2014, 3:53:55 PM

Confirmations

6,291,803

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

3a670b5688b2a510f24265f23f434ea8388ad869c615d28a9d1862f6f05a9dd6

Transactions (5)

Coinbase872a8246744702…6c9827981de254

1 in → 1 out8.5200 XPM116 B

AbwWkWZt…kawDhufa

25b6fa2052be4f…1ae3fafc1964ff

1 in → 2 out8.4900 XPM225 B

AY3uU7Kg…d2PEx7M3 AM8GuxnN…AfjbhWoV

785c3d50d14959…614b9e5bfc015a

1 in → 2 out4.8178 XPM226 B

Ae7YXEyn…hnSYZsCr AK4ZWJhJ…BL6FQNHr

1db51182f6a4d8…04f22dd481aec7

1 in → 2 out5.4413 XPM226 B

AWaxTsag…PL1cyPDP AGEaxXwh…Qxy46N61

b769151086f0c9…21b154a47bf664

2 in → 2 out1.1730 XPM373 B

AG8u7ddV…cU5QJSqk APno71jw…Zdd8auDm

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.

4.083 × 10⁹⁹(100-digit number)

40839707589327117587…74187949985004650239

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

4.083 × 10⁹⁹(100-digit number)

40839707589327117587…74187949985004650239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.083 × 10⁹⁹(100-digit number)

40839707589327117587…74187949985004650241

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

8.167 × 10⁹⁹(100-digit number)

81679415178654235174…48375899970009300479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.167 × 10⁹⁹(100-digit number)

81679415178654235174…48375899970009300481

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

1.633 × 10¹⁰⁰(101-digit number)

16335883035730847034…96751799940018600959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.633 × 10¹⁰⁰(101-digit number)

16335883035730847034…96751799940018600961

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

3.267 × 10¹⁰⁰(101-digit number)

32671766071461694069…93503599880037201919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.267 × 10¹⁰⁰(101-digit number)

32671766071461694069…93503599880037201921

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

6.534 × 10¹⁰⁰(101-digit number)

65343532142923388139…87007199760074403839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.534 × 10¹⁰⁰(101-digit number)

65343532142923388139…87007199760074403841

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 #516,955

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