Block #277,945

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/27/2013, 7:00:40 PM · Difficulty 9.9676 · 6,567,398 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5295027c4b90fb6a813144182660e5c3d9151c1c483361f58ea36ef7d86c6bf2

View on Chainz ↗

Height

#277,945

Difficulty

9.967619

Transactions

Size

1003 B

Version

Bits

09f7b5e9

Nonce

24,528

Timestamp

11/27/2013, 7:00:40 PM

Confirmations

6,567,398

Mined by

⛏️ =aRAb4AJiNZZJseSXiarf2XXKvP13GQPBiqAhyiP

Merkle Root

02c9f44317727eb6ca65b45df4b6b380a4145cdb254161f0dd2ec95a23fd6c2f

Transactions (1)

Coinbase02c9f44317727e…2ec95a23fd6c2f

1 in → 25 out10.0500 XPM913 B

AJiNZZJs…BiqAhyiP AP5UvYhU…vLTDwkdA ALoTBdfd…F5XubrE3 Aai6TNLM…kQf2QbQd Ad9pSzHt…cpJ3y2zz

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.

1.203 × 10⁹⁵(96-digit number)

12036210269476537128…34488887844414873599

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

1.203 × 10⁹⁵(96-digit number)

12036210269476537128…34488887844414873599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.203 × 10⁹⁵(96-digit number)

12036210269476537128…34488887844414873601

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

2.407 × 10⁹⁵(96-digit number)

24072420538953074256…68977775688829747199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.407 × 10⁹⁵(96-digit number)

24072420538953074256…68977775688829747201

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

4.814 × 10⁹⁵(96-digit number)

48144841077906148513…37955551377659494399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.814 × 10⁹⁵(96-digit number)

48144841077906148513…37955551377659494401

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

9.628 × 10⁹⁵(96-digit number)

96289682155812297026…75911102755318988799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.628 × 10⁹⁵(96-digit number)

96289682155812297026…75911102755318988801

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

1.925 × 10⁹⁶(97-digit number)

19257936431162459405…51822205510637977599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.925 × 10⁹⁶(97-digit number)

19257936431162459405…51822205510637977601

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 #277,945

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