Block #123,776

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/19/2013, 6:18:08 AM · Difficulty 9.7664 · 6,667,167 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7c783f12671ea239041b7b0c286ab41f4b490b4e75dfefe2e160878b3501e99a

View on Chainz ↗

Height

#123,776

Difficulty

9.766395

Transactions

Size

652 B

Version

Bits

09c43279

Nonce

7,818

Timestamp

8/19/2013, 6:18:08 AM

Confirmations

6,667,167

Merkle Root

933fe2c08845fab50cce2b6e9c8bfae173391df487ba27871a65d322ca30bf74

Transactions (3)

Coinbasecd604ea3f06bd0…9057867d4de753

1 in → 1 out10.4900 XPM109 B

Acw7B5Yt…Fk64AjSq

36ec536eefcd56…6432ee2a1c2dfb

1 in → 2 out10.5000 XPM226 B

ALpthvGg…D1g5z4CT AY9fvUj9…wrVgpFxk

f824a4948d266c…c9835413e2b0f4

1 in → 2 out3.3159 XPM225 B

AH9pie7G…1nPiVMu8 AVtj9fEt…5iKvQNA1

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.

9.354 × 10⁹⁹(100-digit number)

93546606148079763723…93650805052181389889

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

9.354 × 10⁹⁹(100-digit number)

93546606148079763723…93650805052181389889

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.354 × 10⁹⁹(100-digit number)

93546606148079763723…93650805052181389891

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

1.870 × 10¹⁰⁰(101-digit number)

18709321229615952744…87301610104362779779

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.870 × 10¹⁰⁰(101-digit number)

18709321229615952744…87301610104362779781

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

3.741 × 10¹⁰⁰(101-digit number)

37418642459231905489…74603220208725559559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.741 × 10¹⁰⁰(101-digit number)

37418642459231905489…74603220208725559561

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

7.483 × 10¹⁰⁰(101-digit number)

74837284918463810979…49206440417451119119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.483 × 10¹⁰⁰(101-digit number)

74837284918463810979…49206440417451119121

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

1.496 × 10¹⁰¹(102-digit number)

14967456983692762195…98412880834902238239

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