Block #122,645

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/18/2013, 2:57:39 PM · Difficulty 9.7565 · 6,672,341 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

dd83d19891b399992d9fa4ee29e4756dea921908c1a7e27439a6318366cf0278

View on Chainz ↗

Height

#122,645

Difficulty

9.756473

Transactions

Size

699 B

Version

Bits

09c1a83d

Nonce

878,838

Timestamp

8/18/2013, 2:57:39 PM

Confirmations

6,672,341

Mined by

⛏️ P2SHAbVbHNSGmdML79Gngw7FXpxqm49XNWJjHc

Merkle Root

91eb82c6856dbb1fa4f02e676014d60ae916e321aa8952da6d5e6ee3537ca4f9

Transactions (3)

Coinbaseba26dd47d07d0a…be6621b75049ec

1 in → 1 out10.5100 XPM109 B

AbVbHNSG…9XNWJjHc

4192c0a9cc1e2c…0b6e31dc2ac41a

2 in → 2 out35.7500 XPM307 B

AM9jeKLb…y7m1jbnT ANT5pk9F…b2YWsxmW

9eede2d82190e3…b46f5cfd8f662a

1 in → 2 out10.5000 XPM191 B

AXUtFnVB…2K4kmJnq AWk73XUD…dKKCWRHV

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.

8.681 × 10⁹⁹(100-digit number)

86818832243295070848…81609695307711083799

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

8.681 × 10⁹⁹(100-digit number)

86818832243295070848…81609695307711083799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.681 × 10⁹⁹(100-digit number)

86818832243295070848…81609695307711083801

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

1.736 × 10¹⁰⁰(101-digit number)

17363766448659014169…63219390615422167599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.736 × 10¹⁰⁰(101-digit number)

17363766448659014169…63219390615422167601

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

3.472 × 10¹⁰⁰(101-digit number)

34727532897318028339…26438781230844335199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.472 × 10¹⁰⁰(101-digit number)

34727532897318028339…26438781230844335201

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

6.945 × 10¹⁰⁰(101-digit number)

69455065794636056678…52877562461688670399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.945 × 10¹⁰⁰(101-digit number)

69455065794636056678…52877562461688670401

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

1.389 × 10¹⁰¹(102-digit number)

13891013158927211335…05755124923377340799

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