Block #406,985

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/16/2014, 3:26:03 PM · Difficulty 10.4332 · 6,399,388 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

958bb61b591e437cce1abc936ce09af4fa5b02887b46934cb088826251dae3ae

View on Chainz ↗

Height

#406,985

Difficulty

10.433238

Transactions

Size

768 B

Version

Bits

0a6ee8b1

Nonce

552,502

Timestamp

2/16/2014, 3:26:03 PM

Confirmations

6,399,388

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

bdb6be010712fd8b02ecf5b8625ef8d0a9b1ec61eeb4d1f975657fc4f42888c0

Transactions (3)

Coinbase7b6b9a9c33cdfb…7cf4ffcfae9c69

1 in → 1 out9.1901 XPM110 B

AeKNrjNj…1NEq95Ta

6945aaae19a6e1…2f40e03168d5eb

2 in → 1 out6.1339 XPM340 B

Ad8gSQeu…p2ekK722

a60afd05f28c53…1df5bf1903f235

1 in → 2 out5.0917 XPM225 B

AWjMy3MQ…6SDvk22A AYuZEJKf…mWKn3L7S

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.

1.666 × 10¹⁰²(103-digit number)

16669536514321238447…44885559479934069919

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

1.666 × 10¹⁰²(103-digit number)

16669536514321238447…44885559479934069919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.666 × 10¹⁰²(103-digit number)

16669536514321238447…44885559479934069921

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

3.333 × 10¹⁰²(103-digit number)

33339073028642476895…89771118959868139839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.333 × 10¹⁰²(103-digit number)

33339073028642476895…89771118959868139841

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

6.667 × 10¹⁰²(103-digit number)

66678146057284953791…79542237919736279679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.667 × 10¹⁰²(103-digit number)

66678146057284953791…79542237919736279681

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

1.333 × 10¹⁰³(104-digit number)

13335629211456990758…59084475839472559359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.333 × 10¹⁰³(104-digit number)

13335629211456990758…59084475839472559361

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

2.667 × 10¹⁰³(104-digit number)

26671258422913981516…18168951678945118719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.667 × 10¹⁰³(104-digit number)

26671258422913981516…18168951678945118721

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 #406,985

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