Block #123,109

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/18/2013, 9:05:37 PM · Difficulty 9.7610 · 6,694,219 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

923cd7fafbbfc89cf496861e2692c48b0f2ccff9b2ef6174dc4af3d52ffb2499

View on Chainz ↗

Height

#123,109

Difficulty

9.760953

Transactions

Size

359 B

Version

Bits

09c2cdcb

Nonce

16,346

Timestamp

8/18/2013, 9:05:37 PM

Confirmations

6,694,219

Mined by

⛏️ P2SHAe89LAoDDgDQb6wRkPwUXy2VRdd6GcXXXx

Merkle Root

fda76528372c936a1453161b098a06fe3f3a7acf2d566d9a9410d6c84414f671

Transactions (2)

Coinbasefbf744c6828bac…db86ef54eb2aa6

1 in → 1 out10.4900 XPM109 B

Ae89LAoD…d6GcXXXx

014048959fcaf9…188f0469718d08

1 in → 1 out11.7100 XPM158 B

AUwKMCYC…hHVVSiWv

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.

5.656 × 10⁹⁹(100-digit number)

56564788859184670401…25769290266570059999

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

5.656 × 10⁹⁹(100-digit number)

56564788859184670401…25769290266570059999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.656 × 10⁹⁹(100-digit number)

56564788859184670401…25769290266570060001

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

1.131 × 10¹⁰⁰(101-digit number)

11312957771836934080…51538580533140119999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.131 × 10¹⁰⁰(101-digit number)

11312957771836934080…51538580533140120001

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

2.262 × 10¹⁰⁰(101-digit number)

22625915543673868160…03077161066280239999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.262 × 10¹⁰⁰(101-digit number)

22625915543673868160…03077161066280240001

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

4.525 × 10¹⁰⁰(101-digit number)

45251831087347736320…06154322132560479999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.525 × 10¹⁰⁰(101-digit number)

45251831087347736320…06154322132560480001

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

9.050 × 10¹⁰⁰(101-digit number)

90503662174695472641…12308644265120959999

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

Block #123,109

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