Block #121,928

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/18/2013, 3:49:00 AM · Difficulty 9.7540 · 6,681,700 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

dbd20345b4af882c21747663c4a302d974734be7f253875bf73fccd957fea4ed

View on Chainz ↗

Height

#121,928

Difficulty

9.754015

Transactions

Size

393 B

Version

Bits

09c10725

Nonce

200,524

Timestamp

8/18/2013, 3:49:00 AM

Confirmations

6,681,700

Mined by

⛏️ P2SHAezMwyLP2hpT3yh3LDZkydqkpsrTg7Eyfk

Merkle Root

a48068c98cc1ab2f832d34926a736d2e44bc2dc95faca2dd723b8561b20c3b34

Transactions (2)

Coinbase1106a6f583a386…09458834f46344

1 in → 1 out10.5100 XPM109 B

AezMwyLP…rTg7Eyfk

3a6c4405ab8785…cda64fa5984a09

1 in → 2 out10.4900 XPM192 B

AXUtFnVB…2K4kmJnq AP4UDTjC…EGQVy6UQ

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.

2.106 × 10⁹⁸(99-digit number)

21066884999483612316…38140095262813119049

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

2.106 × 10⁹⁸(99-digit number)

21066884999483612316…38140095262813119049

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.106 × 10⁹⁸(99-digit number)

21066884999483612316…38140095262813119051

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

4.213 × 10⁹⁸(99-digit number)

42133769998967224633…76280190525626238099

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.213 × 10⁹⁸(99-digit number)

42133769998967224633…76280190525626238101

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

8.426 × 10⁹⁸(99-digit number)

84267539997934449266…52560381051252476199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.426 × 10⁹⁸(99-digit number)

84267539997934449266…52560381051252476201

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

1.685 × 10⁹⁹(100-digit number)

16853507999586889853…05120762102504952399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.685 × 10⁹⁹(100-digit number)

16853507999586889853…05120762102504952401

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

3.370 × 10⁹⁹(100-digit number)

33707015999173779706…10241524205009904799

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