Block #605,469

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/28/2014, 1:05:11 PM · Difficulty 10.9099 · 6,202,112 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c4e7b6dbd23690e3073ac7bc05be9ef92bd2a432654e646aa0e9bb1b830d8b06

View on Chainz ↗

Height

#605,469

Difficulty

10.909906

Transactions

Size

806 B

Version

Bits

0ae8ef92

Nonce

784,383,021

Timestamp

6/28/2014, 1:05:11 PM

Confirmations

6,202,112

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

e7ed957b93a2d71d7a7a7521aa58a7b90b757dfdefd1bb879541ddcae4e873d3

Transactions (3)

Coinbase43561297aadfae…123283bc125c9d

1 in → 1 out8.4100 XPM116 B

ANSXnLY2…Sd25TjkD

95c967ac82349b…f9a1cff57e16d1

1 in → 3 out8.3400 XPM225 B

AeKNrjNj…1NEq95Ta AMXQrWx5…XSxNgyAS AKy4P26p…bxEZW13i

ea3b235632d320…ba49ec38b7209e

2 in → 2 out0.5165 XPM373 B

AZobZSiK…m2bPFEmz AMkCa7e8…am94JpJu

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.

2.898 × 10⁹⁹(100-digit number)

28981260580393066125…74241130828206026239

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

2.898 × 10⁹⁹(100-digit number)

28981260580393066125…74241130828206026239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.898 × 10⁹⁹(100-digit number)

28981260580393066125…74241130828206026241

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

5.796 × 10⁹⁹(100-digit number)

57962521160786132251…48482261656412052479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.796 × 10⁹⁹(100-digit number)

57962521160786132251…48482261656412052481

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

1.159 × 10¹⁰⁰(101-digit number)

11592504232157226450…96964523312824104959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.159 × 10¹⁰⁰(101-digit number)

11592504232157226450…96964523312824104961

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

2.318 × 10¹⁰⁰(101-digit number)

23185008464314452900…93929046625648209919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.318 × 10¹⁰⁰(101-digit number)

23185008464314452900…93929046625648209921

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

4.637 × 10¹⁰⁰(101-digit number)

46370016928628905801…87858093251296419839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.637 × 10¹⁰⁰(101-digit number)

46370016928628905801…87858093251296419841

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 #605,469

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