Block #395,507

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/8/2014, 6:41:16 PM · Difficulty 10.4108 · 6,412,324 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

577db6c687b7b5757da04bad8bd20021a876d33b624a0d920f31ea7466f1097f

View on Chainz ↗

Height

#395,507

Difficulty

10.410781

Transactions

Size

972 B

Version

Bits

0a6928ea

Nonce

454,735

Timestamp

2/8/2014, 6:41:16 PM

Confirmations

6,412,324

Mined by

ATp4jJhsSxZ4c3nv24ZhThTqRXTbSgR8Qb

Merkle Root

dc44a263740197c0c6b07a5328965d5443bc7572830d7bbd602e83e908c15ad7

Transactions (1)

Coinbasedc44a263740197…2e83e908c15ad7

1 in → 24 out9.2100 XPM879 B

ATp4jJhs…TbSgR8Qb AbPcCMg4…719q6mAX AHarCvsi…g9VwtVzV AMunqLwt…nFnv4dvR ALzHt7oX…RZYifDqk

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.

1.300 × 10¹⁰²(103-digit number)

13006315027105308680…80108852256877419199

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

1.300 × 10¹⁰²(103-digit number)

13006315027105308680…80108852256877419199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.300 × 10¹⁰²(103-digit number)

13006315027105308680…80108852256877419201

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

2.601 × 10¹⁰²(103-digit number)

26012630054210617361…60217704513754838399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.601 × 10¹⁰²(103-digit number)

26012630054210617361…60217704513754838401

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

5.202 × 10¹⁰²(103-digit number)

52025260108421234722…20435409027509676799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.202 × 10¹⁰²(103-digit number)

52025260108421234722…20435409027509676801

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

1.040 × 10¹⁰³(104-digit number)

10405052021684246944…40870818055019353599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.040 × 10¹⁰³(104-digit number)

10405052021684246944…40870818055019353601

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

2.081 × 10¹⁰³(104-digit number)

20810104043368493888…81741636110038707199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.081 × 10¹⁰³(104-digit number)

20810104043368493888…81741636110038707201

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 #395,507

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