Block #939,496

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 2/16/2015, 10:09:31 PM · Difficulty 10.9008 · 5,863,524 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0a8858eab8a1752b87606a7d1bb7405a7e07294a68e8b019252b17e483977128

View on Chainz ↗

Height

#939,496

Difficulty

10.900776

Transactions

Size

2.27 KB

Version

Bits

0ae69946

Nonce

93,665,399

Timestamp

2/16/2015, 10:09:31 PM

Confirmations

5,863,524

Mined by

⛏️ P2SHAK5YgSjPDRYkgGQqU1jfnz6fPyJubooUrw

Merkle Root

a12e12bca2918b0fba22018e3d5696821a4e1b2a8a3757ebdbd3a3bb8e4c2bf7

Transactions (4)

Coinbase70efca3db8d4ac…7b53257da701ad

1 in → 1 out8.4443 XPM109 B

AK5YgSjP…JubooUrw

69557cadbfd5ac…a57384bd4bc736

4 in → 2 out32.1905 XPM670 B

AVJBBZdG…akqZhWxg AHZkUHtR…EUjZu7Tf

7f1bafa8fde4cc…c4300d77fbc270

8 in → 1 out0.1248 XPM1.20 KB

APDFiiZT…oqxnymU8

a4f8189aa262a8…62e882dd2d7ee4

1 in → 2 out0.8905 XPM225 B

AThT6FXk…zUtqbV3o AHRoBSh4…BSVTQ36Q

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.

2.776 × 10⁹⁵(96-digit number)

27760591338082784637…98413696247226937119

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

2.776 × 10⁹⁵(96-digit number)

27760591338082784637…98413696247226937119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.776 × 10⁹⁵(96-digit number)

27760591338082784637…98413696247226937121

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

5.552 × 10⁹⁵(96-digit number)

55521182676165569275…96827392494453874239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.552 × 10⁹⁵(96-digit number)

55521182676165569275…96827392494453874241

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

1.110 × 10⁹⁶(97-digit number)

11104236535233113855…93654784988907748479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.110 × 10⁹⁶(97-digit number)

11104236535233113855…93654784988907748481

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

2.220 × 10⁹⁶(97-digit number)

22208473070466227710…87309569977815496959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.220 × 10⁹⁶(97-digit number)

22208473070466227710…87309569977815496961

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

4.441 × 10⁹⁶(97-digit number)

44416946140932455420…74619139955630993919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.441 × 10⁹⁶(97-digit number)

44416946140932455420…74619139955630993921

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

8.883 × 10⁹⁶(97-digit number)

88833892281864910840…49238279911261987839

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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