Block #28,058

TWNLength 7★☆☆☆☆

Bi-Twin Chain · Discovered 7/13/2013, 10:59:30 AM · Difficulty 7.9808 · 6,778,251 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cc8dc5d30b1bc1bc5375c6ef78d182465119ef040442cf5fd6c7452e341ddff1

View on Chainz ↗

Height

#28,058

Difficulty

7.980796

Transactions

Size

916 B

Version

Bits

07fb1578

Nonce

256

Timestamp

7/13/2013, 10:59:30 AM

Confirmations

6,778,251

Mined by

⛏️ P2SHAY9SWyHUiy1GfRLreBxA2qBGkpXWzxeER3

Merkle Root

5faf04235d7a999842384a653b4f96952cca1706ba5bb0d3ef59cb3d392fd244

Transactions (2)

Coinbased49e82dbf18f5e…400fe93c55a078

1 in → 1 out15.6900 XPM108 B

AY9SWyHU…XWzxeER3

8f7e31a46ab70d…078aabdbd231c5

5 in → 2 out77.0374 XPM717 B

AYk1sVe4…9pfa3fBu AbqhPreq…XpwZBVMa

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.

5.450 × 10⁹⁷(98-digit number)

54502556511574347438…73903165010450592449

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

5.450 × 10⁹⁷(98-digit number)

54502556511574347438…73903165010450592449

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.450 × 10⁹⁷(98-digit number)

54502556511574347438…73903165010450592451

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

1.090 × 10⁹⁸(99-digit number)

10900511302314869487…47806330020901184899

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.090 × 10⁹⁸(99-digit number)

10900511302314869487…47806330020901184901

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

2.180 × 10⁹⁸(99-digit number)

21801022604629738975…95612660041802369799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.180 × 10⁹⁸(99-digit number)

21801022604629738975…95612660041802369801

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

4.360 × 10⁹⁸(99-digit number)

43602045209259477950…91225320083604739599

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 7 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

CommonChain length 7

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #28,058

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