Block #438,817

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/11/2014, 6:49:32 AM · Difficulty 10.3558 · 6,367,686 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f4c65f95ccda58758de52ffe03c129c4ddd6da91f07a57c8345eecf3be4ca1a0

View on Chainz ↗

Height

#438,817

Difficulty

10.355773

Transactions

Size

14.19 KB

Version

Bits

0a5b13ea

Nonce

475,412

Timestamp

3/11/2014, 6:49:32 AM

Confirmations

6,367,686

Mined by

⛏️ P2SHASXb8Msj7tnyLvWQxYzaaZ1YewBxGf64iZ

Merkle Root

7fee8b3ef3a558e0361a4ea5e1cd49f2e26304308f2f030cfc5d8c0429ac9d75

Transactions (3)

Coinbasea6cc4d807dc0e0…3fcaa1db3517fe

1 in → 1 out9.4700 XPM101 B

ASXb8Msj…BxGf64iZ

b329fbd2c747b3…b420c510aa6bb5

89 in → 2 out29.6765 XPM12.94 KB

AHYwP5gM…jqbB9CK6 Acew4a4q…nz8ihKiX

c094f72fb0975f…d9813ddbae47c1

5 in → 15 out47.6900 XPM1.06 KB

AVkQZ7QV…nyXdtfJY AUbuMqhM…Yi6edrK9 ARqTx3uQ…WSkyk2K3 APeoSKP6…QVsJJKDK AbJAcEfw…PkVprLzT

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.

7.899 × 10⁹⁶(97-digit number)

78990343105540633441…94842750915538703199

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

7.899 × 10⁹⁶(97-digit number)

78990343105540633441…94842750915538703199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.899 × 10⁹⁶(97-digit number)

78990343105540633441…94842750915538703201

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

1.579 × 10⁹⁷(98-digit number)

15798068621108126688…89685501831077406399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.579 × 10⁹⁷(98-digit number)

15798068621108126688…89685501831077406401

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

3.159 × 10⁹⁷(98-digit number)

31596137242216253376…79371003662154812799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.159 × 10⁹⁷(98-digit number)

31596137242216253376…79371003662154812801

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

6.319 × 10⁹⁷(98-digit number)

63192274484432506753…58742007324309625599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.319 × 10⁹⁷(98-digit number)

63192274484432506753…58742007324309625601

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

1.263 × 10⁹⁸(99-digit number)

12638454896886501350…17484014648619251199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.263 × 10⁹⁸(99-digit number)

12638454896886501350…17484014648619251201

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 #438,817

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