Block #440,948

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/12/2014, 6:50:55 PM · Difficulty 10.3536 · 6,369,435 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3c8c0b694302cdd8d53bc8df25d0f1cb932a8040526597266edf7f6177262b61

View on Chainz ↗

Height

#440,948

Difficulty

10.353600

Transactions

Size

2.27 KB

Version

Bits

0a5a8583

Nonce

389,770

Timestamp

3/12/2014, 6:50:55 PM

Confirmations

6,369,435

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

4b6dd4e2c27d0cb6661b43aea8fd2495720033fe05265e9db10cc21a7cdca2d7

Transactions (4)

Coinbase2ee580cf6b16ef…ceef2e36d82e98

1 in → 1 out9.3583 XPM110 B

AeKNrjNj…1NEq95Ta

c6f3c0476179a6…fc73df4cab8f30

9 in → 2 out27.3158 XPM1.38 KB

AcqV6J4W…dRYXwABC AMWFCHWv…DYBPW2Yq

ae8d9c5ea610c3…2ffb2c162a879f

2 in → 2 out3.0922 XPM374 B

AHzs1Cpa…6T1Y8LzN AS35yQ1k…zuqiYCQR

8482396249c6fc…b11286b792b22e

2 in → 1 out0.5500 XPM340 B

AcMdZXM2…MRf2mBpL

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.

6.048 × 10¹⁰⁰(101-digit number)

60487689509563199871…09090556035996180479

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

6.048 × 10¹⁰⁰(101-digit number)

60487689509563199871…09090556035996180479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.048 × 10¹⁰⁰(101-digit number)

60487689509563199871…09090556035996180481

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

1.209 × 10¹⁰¹(102-digit number)

12097537901912639974…18181112071992360959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.209 × 10¹⁰¹(102-digit number)

12097537901912639974…18181112071992360961

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

2.419 × 10¹⁰¹(102-digit number)

24195075803825279948…36362224143984721919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.419 × 10¹⁰¹(102-digit number)

24195075803825279948…36362224143984721921

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

4.839 × 10¹⁰¹(102-digit number)

48390151607650559897…72724448287969443839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.839 × 10¹⁰¹(102-digit number)

48390151607650559897…72724448287969443841

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

9.678 × 10¹⁰¹(102-digit number)

96780303215301119794…45448896575938887679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.678 × 10¹⁰¹(102-digit number)

96780303215301119794…45448896575938887681

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 #440,948

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