Block #545,905

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/15/2014, 2:48:17 PM · Difficulty 10.9547 · 6,250,398 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3ae3bb2a4c2bdf1abdc9513acc1c03dffa66c90c33bf7105d04d3e14b355aa4d

View on Chainz ↗

Height

#545,905

Difficulty

10.954651

Transactions

Size

3.98 KB

Version

Bits

0af46403

Nonce

1,047,321

Timestamp

5/15/2014, 2:48:17 PM

Confirmations

6,250,398

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

ad14d64c57847971d2f9894376fca1a9af6254536484f7e06585cd6cb6af0971

Transactions (5)

Coinbase99d89e3312d5d4…a5c47e91a7b192

1 in → 1 out8.3800 XPM116 B

ANSXnLY2…Sd25TjkD

94dfa5fd0f9bce…772583cc1d7f89

15 in → 2 out67.1338 XPM2.24 KB

AcpYzhW7…xBAQBNdQ ANVXk6zx…bFLZWtpW

e68e25d5184761…3f541d2180be66

4 in → 2 out30.0230 XPM671 B

AWjZW3Cw…ySK7iwvM ANdS239e…ewnZjA46

526a3dff217de3…143bf361cf217f

1 in → 3 out8.3700 XPM226 B

AHDTi5u9…w5TNUkX7 AeKNrjNj…1NEq95Ta AUfa5LFJ…C4BhhWGa

79e1c6d4e113ad…c88475f17eb5d8

4 in → 2 out0.5480 XPM670 B

Aa3tkcHK…RkxX1aHk AMuYYsgd…ioD1TEUt

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.

2.290 × 10¹⁰⁰(101-digit number)

22902957450929432821…09754650339675494399

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

2.290 × 10¹⁰⁰(101-digit number)

22902957450929432821…09754650339675494399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.290 × 10¹⁰⁰(101-digit number)

22902957450929432821…09754650339675494401

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

4.580 × 10¹⁰⁰(101-digit number)

45805914901858865642…19509300679350988799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.580 × 10¹⁰⁰(101-digit number)

45805914901858865642…19509300679350988801

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

9.161 × 10¹⁰⁰(101-digit number)

91611829803717731285…39018601358701977599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.161 × 10¹⁰⁰(101-digit number)

91611829803717731285…39018601358701977601

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

1.832 × 10¹⁰¹(102-digit number)

18322365960743546257…78037202717403955199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.832 × 10¹⁰¹(102-digit number)

18322365960743546257…78037202717403955201

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

3.664 × 10¹⁰¹(102-digit number)

36644731921487092514…56074405434807910399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.664 × 10¹⁰¹(102-digit number)

36644731921487092514…56074405434807910401

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

7.328 × 10¹⁰¹(102-digit number)

73289463842974185028…12148810869615820799

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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