Block #545,400

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/15/2014, 9:00:19 AM · Difficulty 10.9532 · 6,279,553 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6aee9bb7fc8ac0201efdf95950a4e7d0e2667cb40c52c067cbf494276659f3ca

View on Chainz ↗

Height

#545,400

Difficulty

10.953207

Transactions

Size

47.34 KB

Version

Bits

0af40560

Nonce

29,877,643

Timestamp

5/15/2014, 9:00:19 AM

Confirmations

6,279,553

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

5dc3322df7f6821c2df5c2540ddb674942f9d28621b7f84a3f6b024d2c7814c4

Transactions (5)

Coinbase2cd5ac85b2037e…4b9dc3c49227a1

1 in → 1 out8.8500 XPM116 B

ANSXnLY2…Sd25TjkD

8d00958f67c209…db1998dfc477d5

321 in → 2 out50.0100 XPM46.47 KB

ATXUzdyn…ro27aB9M AQdNfKD5…isPXUJaK

13f5ec7a417670…9e157b903064a4

1 in → 2 out6.2516 XPM225 B

AdGrXCNy…13z3uNx3 Ac4zTME1…gVZfyoXZ

9b208942aa0db4…e8e7675c942891

1 in → 2 out3.8061 XPM225 B

AKweJ6z4…fiQLQ8zk AU7JoCG4…x1MQqScc

062bef11deaeab…78442b1728707b

1 in → 2 out5.2233 XPM226 B

AZxkSxov…9uoWycVz Aen97Bzy…Em2nVveP

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.

8.279 × 10¹⁰¹(102-digit number)

82797717099451230207…02388019058562170879

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

8.279 × 10¹⁰¹(102-digit number)

82797717099451230207…02388019058562170879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.279 × 10¹⁰¹(102-digit number)

82797717099451230207…02388019058562170881

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

1.655 × 10¹⁰²(103-digit number)

16559543419890246041…04776038117124341759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.655 × 10¹⁰²(103-digit number)

16559543419890246041…04776038117124341761

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

3.311 × 10¹⁰²(103-digit number)

33119086839780492083…09552076234248683519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.311 × 10¹⁰²(103-digit number)

33119086839780492083…09552076234248683521

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

6.623 × 10¹⁰²(103-digit number)

66238173679560984166…19104152468497367039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.623 × 10¹⁰²(103-digit number)

66238173679560984166…19104152468497367041

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

1.324 × 10¹⁰³(104-digit number)

13247634735912196833…38208304936994734079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.324 × 10¹⁰³(104-digit number)

13247634735912196833…38208304936994734081

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

2.649 × 10¹⁰³(104-digit number)

26495269471824393666…76416609873989468159

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

Block #545,400

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