Block #379,786

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/28/2014, 6:35:09 PM · Difficulty 10.4202 · 6,436,756 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

51793298ea606a531c3fdbc476471e29652ff2890e5d2f32f84e30e9d3797762

View on Chainz ↗

Height

#379,786

Difficulty

10.420203

Transactions

Size

1.85 KB

Version

Bits

0a6b926e

Nonce

129,067

Timestamp

1/28/2014, 6:35:09 PM

Confirmations

6,436,756

Mined by

⛏️ HAMunqLwthHK9wFBkLrPo9zCxVfnFnv4dvR

Merkle Root

4f3d83c151623f1245bcbd423cc926d2ca4242df5678d38628fc53470f39b813

Transactions (5)

Coinbase1f9474ea733634…a2faa6890953ec

1 in → 20 out9.2400 XPM743 B

AMunqLwt…nFnv4dvR AUzEPJFG…kYkA5U9V ATLD7BNP…nPjXCb2h AXiARuCQ…E8J7Rsas AU9KdB9r…o5XC6WMy

c8ad5fc63de2db…714ad48ffe411f

2 in → 2 out15.3742 XPM374 B

Adv4KUrF…bzQ1B12f AVY1T7W7…AkdMXMfG

eea3613385d0a7…15e6df7a927449

1 in → 2 out6.3655 XPM227 B

AWHmjNyM…fUmHr4Kd AVfYRY4k…VnTR3zCW

fb8c98f3ffc04d…a634695ee43ed9

1 in → 2 out3.0348 XPM226 B

AT9fq4Cd…F14Z2LDT AdhUErGY…P6SsFaVU

cb9cd447819725…c27a3ad8d10e77

1 in → 2 out4.1060 XPM227 B

AXPAMG6v…taswyxcg AWHmWKJx…r6kT2axo

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.

7.384 × 10¹⁰²(103-digit number)

73847481414467148016…69493062135440598559

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

7.384 × 10¹⁰²(103-digit number)

73847481414467148016…69493062135440598559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.384 × 10¹⁰²(103-digit number)

73847481414467148016…69493062135440598561

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

1.476 × 10¹⁰³(104-digit number)

14769496282893429603…38986124270881197119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.476 × 10¹⁰³(104-digit number)

14769496282893429603…38986124270881197121

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

2.953 × 10¹⁰³(104-digit number)

29538992565786859206…77972248541762394239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.953 × 10¹⁰³(104-digit number)

29538992565786859206…77972248541762394241

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

5.907 × 10¹⁰³(104-digit number)

59077985131573718413…55944497083524788479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.907 × 10¹⁰³(104-digit number)

59077985131573718413…55944497083524788481

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

1.181 × 10¹⁰⁴(105-digit number)

11815597026314743682…11888994167049576959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.181 × 10¹⁰⁴(105-digit number)

11815597026314743682…11888994167049576961

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 #379,786

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