Block #438,678

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/11/2014, 4:37:58 AM · Difficulty 10.3551 · 6,387,637 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

109370c0b5d37298ff2170c8014bb065b89bdbbeafb0c2c3f385bb1f893a7fa4

View on Chainz ↗

Height

#438,678

Difficulty

10.355058

Transactions

Size

2.18 KB

Version

Bits

0a5ae51d

Nonce

33,847

Timestamp

3/11/2014, 4:37:58 AM

Confirmations

6,387,637

Mined by

⛏️ qAdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

b9faba15d1c827d5cf6eacb69d453f9c2a349cbac8b643b02bfd3883a6857aed

Transactions (3)

Coinbasec967df040ae7b7…8e2ba9f7607c6f

1 in → 23 out9.3300 XPM845 B

AdFLJFhb…bsaVkAyh ASgUri65…C7NLcyBg AGz9gyZW…bo8NYQpw AUFKXvnz…342ApNcm AXCpMYgL…1r94ZQDa

497978bde2c05c…52676d3016b451

2 in → 7 out18.6200 XPM478 B

ATVxJHqC…6v7Pqgka AW4KSrp3…1PTneMrf AdipcxVo…qAZrfiDs AeKNrjNj…1NEq95Ta AP8xnw8a…fhaMMjoo

ef80ca2d91f77e…5676a8b08e6990

5 in → 2 out13.0875 XPM819 B

ANDdW4Q4…R8vuwSJR AJsi4goD…PBWtgQcM

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.

6.807 × 10⁹⁸(99-digit number)

68072400574524844929…32507642828055380799

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

6.807 × 10⁹⁸(99-digit number)

68072400574524844929…32507642828055380799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.807 × 10⁹⁸(99-digit number)

68072400574524844929…32507642828055380801

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

1.361 × 10⁹⁹(100-digit number)

13614480114904968985…65015285656110761599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.361 × 10⁹⁹(100-digit number)

13614480114904968985…65015285656110761601

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

2.722 × 10⁹⁹(100-digit number)

27228960229809937971…30030571312221523199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.722 × 10⁹⁹(100-digit number)

27228960229809937971…30030571312221523201

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

5.445 × 10⁹⁹(100-digit number)

54457920459619875943…60061142624443046399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.445 × 10⁹⁹(100-digit number)

54457920459619875943…60061142624443046401

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

1.089 × 10¹⁰⁰(101-digit number)

10891584091923975188…20122285248886092799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.089 × 10¹⁰⁰(101-digit number)

10891584091923975188…20122285248886092801

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 #438,678

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