Block #354,951

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 1/11/2014, 8:35:52 PM · Difficulty 10.3530 · 6,456,000 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

dc51ca56ac30ed525607f01f6f786ae57f0ea4621bc8a29728c7b6a96b507b8a

View on Chainz ↗

Height

#354,951

Difficulty

10.353020

Transactions

Size

2.95 KB

Version

Bits

0a5a5f8a

Nonce

92,306

Timestamp

1/11/2014, 8:35:52 PM

Confirmations

6,456,000

Mined by

⛏️ jaRAQwRN8bEjE7sawFBq7N38V9niAV8PsTcY9

Merkle Root

336698150c50e9744ecafbca1a1b0ad3e6487808ee081b2ebe59f062f3b130a9

Transactions (4)

Coinbasef41cb8df3687a9…685f019775b83c

1 in → 25 out9.3200 XPM912 B

AQwRN8bE…V8PsTcY9 Aac9Hjdg…P4ktypc3 AYtDvcGs…VuAcA7m7 AZV4TwxQ…8JnQqSoH ATKK7iFz…wZm46KN1

fa34e9d7827fd1…f65f3e48660e16

8 in → 16 out47.4349 XPM1.53 KB

AQf75Tco…RiRB1iEd AFtcWwpC…9iGwBJS1 Ab4UHUTw…ebenAHnu Aacswgin…gyBaWE7b APSoHXZY…kNZx697r

f195c1ae7124f1…465764c826479d

1 in → 2 out4.3504 XPM227 B

AXhWtbPt…5LyuGMVA AL9E6V3g…HmmXb3zS

dd6bf19d9ec348…442eb83e334920

1 in → 2 out4.3114 XPM225 B

Aaawt27r…h9RAfLEJ AK5eMZv7…7wDmjJxU

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.

1.377 × 10⁹⁵(96-digit number)

13774989738870455176…33063763592001576959

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

1.377 × 10⁹⁵(96-digit number)

13774989738870455176…33063763592001576959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.377 × 10⁹⁵(96-digit number)

13774989738870455176…33063763592001576961

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

2.754 × 10⁹⁵(96-digit number)

27549979477740910353…66127527184003153919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.754 × 10⁹⁵(96-digit number)

27549979477740910353…66127527184003153921

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

5.509 × 10⁹⁵(96-digit number)

55099958955481820707…32255054368006307839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.509 × 10⁹⁵(96-digit number)

55099958955481820707…32255054368006307841

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

1.101 × 10⁹⁶(97-digit number)

11019991791096364141…64510108736012615679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.101 × 10⁹⁶(97-digit number)

11019991791096364141…64510108736012615681

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

2.203 × 10⁹⁶(97-digit number)

22039983582192728283…29020217472025231359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.203 × 10⁹⁶(97-digit number)

22039983582192728283…29020217472025231361

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

4.407 × 10⁹⁶(97-digit number)

44079967164385456566…58040434944050462719

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 #354,951

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