Block #859,363

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 12/19/2014, 9:47:43 AM · Difficulty 10.9654 · 5,965,139 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c07c4b006ec109ab09c5720a3942447137343c8e4144546520b359210d4edd52

View on Chainz ↗

Height

#859,363

Difficulty

10.965432

Transactions

Size

1.52 KB

Version

Bits

0af72687

Nonce

2,888,157,940

Timestamp

12/19/2014, 9:47:43 AM

Confirmations

5,965,139

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

b6f9ea19c48b551f78a325d21379f102aae04aa1823cdeb733a855a6690a2aeb

Transactions (5)

Coinbase19164a065bd023…55e28758b13e62

1 in → 1 out8.3400 XPM116 B

ANSXnLY2…Sd25TjkD

050a5c72ec25c2…894f9e96e15565

3 in → 2 out1696.5100 XPM521 B

AJ3rZCKj…6FXa2WUe AGf4bxML…tCqWcVMH

a6e2442f9e7eb1…26052229a90e28

1 in → 2 out8.2800 XPM226 B

AaGzfr9m…Z5HThiDz AHRoBSh4…BSVTQ36Q

69596f683a37bf…6dba6ff7884dc6

1 in → 2 out8.2800 XPM227 B

AJHFbK2Q…oeZLfcJD ALP6szJY…eEPSo5sX

0f4a1cde81f500…2bba398efa69dc

2 in → 2 out16.6100 XPM375 B

AeSCDTjX…MwtoboZd APLNtiRX…AsYiY8EA

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.

4.389 × 10⁹⁹(100-digit number)

43890999684049658405…47827168991729582079

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

4.389 × 10⁹⁹(100-digit number)

43890999684049658405…47827168991729582079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.389 × 10⁹⁹(100-digit number)

43890999684049658405…47827168991729582081

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

8.778 × 10⁹⁹(100-digit number)

87781999368099316811…95654337983459164159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.778 × 10⁹⁹(100-digit number)

87781999368099316811…95654337983459164161

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

1.755 × 10¹⁰⁰(101-digit number)

17556399873619863362…91308675966918328319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.755 × 10¹⁰⁰(101-digit number)

17556399873619863362…91308675966918328321

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

3.511 × 10¹⁰⁰(101-digit number)

35112799747239726724…82617351933836656639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.511 × 10¹⁰⁰(101-digit number)

35112799747239726724…82617351933836656641

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

7.022 × 10¹⁰⁰(101-digit number)

70225599494479453449…65234703867673313279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.022 × 10¹⁰⁰(101-digit number)

70225599494479453449…65234703867673313281

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

1.404 × 10¹⁰¹(102-digit number)

14045119898895890689…30469407735346626559

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 #859,363

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