Block #827,189

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/25/2014, 8:59:35 AM · Difficulty 10.9778 · 5,978,614 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d266f487a9600fb22a8e95a90274e4e8ed5fd71213fdb742f6d82b928100aa93

View on Chainz ↗

Height

#827,189

Difficulty

10.977844

Transactions

Size

1.08 KB

Version

Bits

0afa53fa

Nonce

62,311,943

Timestamp

11/25/2014, 8:59:35 AM

Confirmations

5,978,614

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

f74794ff7f6ccfbe7cc0475f2661c51374cde0d8582d93f47fd77cb9c785ceeb

Transactions (5)

Coinbase8f5000314c6cbd…80e30acabac93a

1 in → 1 out8.3200 XPM116 B

ANSXnLY2…Sd25TjkD

16fe111f2cca3b…bf530db1f7a2aa

1 in → 2 out5.3740 XPM227 B

AWvDPNDh…ihGN2yuQ AU5RZLyZ…fbPqsuUB

7d8c527cb6598a…b43a6e7ebb8f03

1 in → 2 out3.2717 XPM225 B

ASQKHu4k…up3Jamr2 AGdWVjRk…LFVsqCnK

71f6307f8d079b…0ec257e8ff31bc

1 in → 2 out3.1061 XPM226 B

AYLAjack…UqpMLQuB ALNQaD7f…2g74yYvV

12321fcd857111…d888aeba7de419

1 in → 2 out1.1315 XPM226 B

Ae7YXEyn…hnSYZsCr AenCcw8B…7fhWV4Si

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.

2.755 × 10⁹⁵(96-digit number)

27552643114106913253…81229599317148879919

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

2.755 × 10⁹⁵(96-digit number)

27552643114106913253…81229599317148879919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.755 × 10⁹⁵(96-digit number)

27552643114106913253…81229599317148879921

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

5.510 × 10⁹⁵(96-digit number)

55105286228213826506…62459198634297759839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.510 × 10⁹⁵(96-digit number)

55105286228213826506…62459198634297759841

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

1.102 × 10⁹⁶(97-digit number)

11021057245642765301…24918397268595519679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.102 × 10⁹⁶(97-digit number)

11021057245642765301…24918397268595519681

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

2.204 × 10⁹⁶(97-digit number)

22042114491285530602…49836794537191039359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.204 × 10⁹⁶(97-digit number)

22042114491285530602…49836794537191039361

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

4.408 × 10⁹⁶(97-digit number)

44084228982571061205…99673589074382078719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.408 × 10⁹⁶(97-digit number)

44084228982571061205…99673589074382078721

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