Block #78,438

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/22/2013, 9:40:52 PM · Difficulty 9.2216 · 6,731,152 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

42944fd68792bfea799f09bd14b388ac0426900c82c16282ce773ea686713c41

View on Chainz ↗

Height

#78,438

Difficulty

9.221606

Transactions

Size

1.65 KB

Version

Bits

0938bb2d

Nonce

246

Timestamp

7/22/2013, 9:40:52 PM

Confirmations

6,731,152

Mined by

⛏️ P2SHAKzXKKExRu2JaxdDQ6Nwor2KVc9pwZrw8f

Merkle Root

507efb6af71f63db64df28ca954f099525e8af54372553860c5392cb0bed566b

Transactions (3)

Coinbase4de16cad06a8fe…670ce3d47f50c5

1 in → 1 out11.7600 XPM110 B

AKzXKKEx…9pwZrw8f

5a635cc3eb20f7…cb193584f074c2

3 in → 2 out12.9657 XPM524 B

AM3u3ToC…AQnAEuat AXBjwq83…XbeTKce7

7042b8c465e70f…448146f624269b

6 in → 2 out133.7136 XPM967 B

AZpbNK13…wLCsgHXm AHpk2NPN…DYZYfm9s

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.

3.547 × 10¹⁰¹(102-digit number)

35471413659602627855…26831126180366710719

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

3.547 × 10¹⁰¹(102-digit number)

35471413659602627855…26831126180366710719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.547 × 10¹⁰¹(102-digit number)

35471413659602627855…26831126180366710721

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

7.094 × 10¹⁰¹(102-digit number)

70942827319205255710…53662252360733421439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.094 × 10¹⁰¹(102-digit number)

70942827319205255710…53662252360733421441

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

1.418 × 10¹⁰²(103-digit number)

14188565463841051142…07324504721466842879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.418 × 10¹⁰²(103-digit number)

14188565463841051142…07324504721466842881

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

2.837 × 10¹⁰²(103-digit number)

28377130927682102284…14649009442933685759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.837 × 10¹⁰²(103-digit number)

28377130927682102284…14649009442933685761

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

5.675 × 10¹⁰²(103-digit number)

56754261855364204568…29298018885867371519

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 #78,438

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