Block #387,569

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/3/2014, 5:37:35 AM · Difficulty 10.4134 · 6,437,989 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

701117ccbec57c185b9500498a922ea1e7c12b580ccb1ebbad2c2dd6baeec84a

View on Chainz ↗

Height

#387,569

Difficulty

10.413386

Transactions

Size

6.06 KB

Version

Bits

0a69d3a8

Nonce

125,379

Timestamp

2/3/2014, 5:37:35 AM

Confirmations

6,437,989

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

00d451035f3a639f8f283d4a26f81aebb8cad65b28b4d5516848aeaf9e3f99fd

Transactions (5)

Coinbase959a35a596b7ff…b4bef0eafcb713

1 in → 1 out9.2900 XPM116 B

AbwWkWZt…kawDhufa

8936075e5bdd68…0eb8686724f20e

5 in → 2 out82.8147 XPM816 B

AMJXCqiv…LcM9rMYU AYNrwg9L…JWHqAeGd

c7f58036b54187…4389961915a9a9

1 in → 2 out9.2200 XPM192 B

AQfTstqN…7m7a1mba AaMRUFMG…S11BNFrC

c55cd81ea25f93…0f787e60d7aa3a

4 in → 7 out18.4853 XPM772 B

Aadjczru…WXPUazmh ALHBdz1N…v6hU6ZDR APinTnXk…ypGZKkAg AeKNrjNj…1NEq95Ta AeR5xAAu…QS19drpA

337409a762b7d4…f24e1b4aeee714

28 in → 2 out28.3591 XPM4.12 KB

AWosy8CS…eMayE3uW AZz7s5FZ…bubYPXww

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.

4.218 × 10¹⁰¹(102-digit number)

42184193257804453380…47124099746413565999

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

4.218 × 10¹⁰¹(102-digit number)

42184193257804453380…47124099746413565999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.218 × 10¹⁰¹(102-digit number)

42184193257804453380…47124099746413566001

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

8.436 × 10¹⁰¹(102-digit number)

84368386515608906760…94248199492827131999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.436 × 10¹⁰¹(102-digit number)

84368386515608906760…94248199492827132001

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

1.687 × 10¹⁰²(103-digit number)

16873677303121781352…88496398985654263999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.687 × 10¹⁰²(103-digit number)

16873677303121781352…88496398985654264001

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

3.374 × 10¹⁰²(103-digit number)

33747354606243562704…76992797971308527999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.374 × 10¹⁰²(103-digit number)

33747354606243562704…76992797971308528001

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

6.749 × 10¹⁰²(103-digit number)

67494709212487125408…53985595942617055999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.749 × 10¹⁰²(103-digit number)

67494709212487125408…53985595942617056001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #387,569

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