Block #288,761

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 12/1/2013, 9:55:19 PM · Difficulty 9.9879 · 6,505,379 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f607b7642088685b1ec096aa47096f688e7cf6e4248b5b0891463f14c2c7d7c4

View on Chainz ↗

Height

#288,761

Difficulty

9.987935

Transactions

Size

1.15 KB

Version

Bits

09fce955

Nonce

351,447

Timestamp

12/1/2013, 9:55:19 PM

Confirmations

6,505,379

Merkle Root

a718d35e035f40ccef4ae58b7c8d02cf6a0dc3aa515365880b77a534ffd0efe7

Transactions (1)

Coinbasea718d35e035f40…77a534ffd0efe7

1 in → 30 out9.9900 XPM1.06 KB

AehEqLuF…x1qVyZ61 AWCkoGXK…zjpfLbCF AFtTtY8N…DgGXX7Cm AXLJzdRc…LJLLZDBD AYPb2Rez…ReMAwnVN

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.

4.151 × 10⁹⁵(96-digit number)

41517006585622651417…30555878497341859839

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

4.151 × 10⁹⁵(96-digit number)

41517006585622651417…30555878497341859839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.151 × 10⁹⁵(96-digit number)

41517006585622651417…30555878497341859841

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

8.303 × 10⁹⁵(96-digit number)

83034013171245302834…61111756994683719679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.303 × 10⁹⁵(96-digit number)

83034013171245302834…61111756994683719681

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

1.660 × 10⁹⁶(97-digit number)

16606802634249060566…22223513989367439359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.660 × 10⁹⁶(97-digit number)

16606802634249060566…22223513989367439361

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

3.321 × 10⁹⁶(97-digit number)

33213605268498121133…44447027978734878719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.321 × 10⁹⁶(97-digit number)

33213605268498121133…44447027978734878721

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

6.642 × 10⁹⁶(97-digit number)

66427210536996242267…88894055957469757439

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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 9

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