Block #33,983

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/14/2013, 5:48:04 AM · Difficulty 7.9927 · 6,774,995 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ea670b08684ac5e0a197bc0633225acad56f469dd5dcb94bd515f14a92000b38

View on Chainz ↗

Height

#33,983

Difficulty

7.992698

Transactions

Size

3.90 KB

Version

Bits

07fe2176

Nonce

192

Timestamp

7/14/2013, 5:48:04 AM

Confirmations

6,774,995

Mined by

⛏️ P2SHAPVAJJpqZGfUFxUrxBPyCiZ8uyuHcypbNH

Merkle Root

259edfd53dd7de01fdff4bcbcf50c9fb44c8660f3fd25ed7fd42402819fbb42f

Transactions (3)

Coinbase6ac4468723e62b…0079ca6c55abc5

1 in → 1 out15.6800 XPM109 B

APVAJJpq…uHcypbNH

34ec7625baff4f…fb7a786ed4220d

2 in → 2 out190.0100 XPM375 B

AHvGyKNr…G7FdFaeZ AHD6Mjdi…D8jKMQcW

bc103b614866de…9de87a6f130fa1

29 in → 2 out439.4600 XPM3.33 KB

Ab4FB6cL…hA3we3FV AaeTAobV…gUsxUMxE

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.

1.741 × 10⁹⁶(97-digit number)

17413727025924053683…86564632109519573519

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

1.741 × 10⁹⁶(97-digit number)

17413727025924053683…86564632109519573519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.741 × 10⁹⁶(97-digit number)

17413727025924053683…86564632109519573521

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

3.482 × 10⁹⁶(97-digit number)

34827454051848107366…73129264219039147039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.482 × 10⁹⁶(97-digit number)

34827454051848107366…73129264219039147041

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

6.965 × 10⁹⁶(97-digit number)

69654908103696214732…46258528438078294079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.965 × 10⁹⁶(97-digit number)

69654908103696214732…46258528438078294081

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

1.393 × 10⁹⁷(98-digit number)

13930981620739242946…92517056876156588159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.393 × 10⁹⁷(98-digit number)

13930981620739242946…92517056876156588161

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 8 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 8

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 #33,983

Cookie Preferences