Block #1,078,329

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/27/2015, 12:42:54 PM · Difficulty 10.7592 · 5,713,407 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

958496d86bbf4b36170618a349e5ca29ce949bfb508d15cd6b702ab0247cbcb0

View on Chainz ↗

Height

#1,078,329

Difficulty

10.759247

Transactions

Size

1.23 KB

Version

Bits

0ac25e09

Nonce

187,514,264

Timestamp

5/27/2015, 12:42:54 PM

Confirmations

5,713,407

Merkle Root

c29772edbbff8e900f61ad98356fa305940e056fa2fe1db597ab9ed25bffda3e

Transactions (5)

Coinbasea6ba702450782b…6fc1d4c51d7d8f

1 in → 1 out8.6600 XPM116 B

ANSXnLY2…Sd25TjkD

1abee2c220bae9…359e01b0e0cd7e

2 in → 2 out11.7116 XPM372 B

AG6mDCE4…1B8281BS Ae9drWdk…FnLTm9Pn

890cbe8646b95c…45c210062d6c37

1 in → 2 out7.0771 XPM225 B

APaYVt8e…rPF99zd2 APhPs9YK…WttrdSKP

5a4ea8b2fa2a0d…71d348face2218

1 in → 2 out5.5853 XPM226 B

AGConaUA…xkaSrFvX Aa4PtTwK…H3ppZFzk

5624b8ccedd632…ce2e4829249215

1 in → 2 out6.0507 XPM226 B

ASL1a5Et…KXtLX2Pr AXrTw46X…e1dGvSFf

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.

2.859 × 10⁹⁶(97-digit number)

28590476427398975287…75755315477941761279

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

2.859 × 10⁹⁶(97-digit number)

28590476427398975287…75755315477941761279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.859 × 10⁹⁶(97-digit number)

28590476427398975287…75755315477941761281

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

5.718 × 10⁹⁶(97-digit number)

57180952854797950575…51510630955883522559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.718 × 10⁹⁶(97-digit number)

57180952854797950575…51510630955883522561

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

1.143 × 10⁹⁷(98-digit number)

11436190570959590115…03021261911767045119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.143 × 10⁹⁷(98-digit number)

11436190570959590115…03021261911767045121

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

2.287 × 10⁹⁷(98-digit number)

22872381141919180230…06042523823534090239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.287 × 10⁹⁷(98-digit number)

22872381141919180230…06042523823534090241

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

4.574 × 10⁹⁷(98-digit number)

45744762283838360460…12085047647068180479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.574 × 10⁹⁷(98-digit number)

45744762283838360460…12085047647068180481

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