Block #277,936

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/27/2013, 6:54:51 PM · Difficulty 9.9676 · 6,516,853 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ed6f77458ad2b40c7800e835ada0509bf642ce292b758df2044e038cc0c2533a

View on Chainz ↗

Height

#277,936

Difficulty

9.967609

Transactions

Size

1.14 KB

Version

Bits

09f7b53e

Nonce

236,356

Timestamp

11/27/2013, 6:54:51 PM

Confirmations

6,516,853

Mined by

⛏️ =aR?KAPeshfYVKJ2qg4aRhC5FMjPmxg3PKcKMKH

Merkle Root

5ffab409a1bf0ddbbd456790c656e9871791df07c37700732e0f61ce8db94aed

Transactions (1)

Coinbase5ffab409a1bf0d…0f61ce8db94aed

1 in → 30 out10.0300 XPM1.06 KB

APeshfYV…3PKcKMKH AN8nUzff…YcDfRDQ2 AbiApRgN…g8QuFUwL AJ9QW1VP…GmAJhvhc AXmS7tZu…11YypHLP

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.

7.681 × 10⁹⁰(91-digit number)

76819275767879511235…70106137746837864699

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

7.681 × 10⁹⁰(91-digit number)

76819275767879511235…70106137746837864699

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.681 × 10⁹⁰(91-digit number)

76819275767879511235…70106137746837864701

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

1.536 × 10⁹¹(92-digit number)

15363855153575902247…40212275493675729399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.536 × 10⁹¹(92-digit number)

15363855153575902247…40212275493675729401

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

3.072 × 10⁹¹(92-digit number)

30727710307151804494…80424550987351458799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.072 × 10⁹¹(92-digit number)

30727710307151804494…80424550987351458801

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

6.145 × 10⁹¹(92-digit number)

61455420614303608988…60849101974702917599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.145 × 10⁹¹(92-digit number)

61455420614303608988…60849101974702917601

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

1.229 × 10⁹²(93-digit number)

12291084122860721797…21698203949405835199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.229 × 10⁹²(93-digit number)

12291084122860721797…21698203949405835201

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