Block #183,856

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/28/2013, 7:14:01 AM · Difficulty 9.8584 · 6,632,748 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e2ce6371c78d29a9af9944d07d264e6e329fef8211d1f0c5cd077ace05fc4026

View on Chainz ↗

Height

#183,856

Difficulty

9.858442

Transactions

Size

686 B

Version

Bits

09dbc2d6

Nonce

4,654

Timestamp

9/28/2013, 7:14:01 AM

Confirmations

6,632,748

Mined by

⛏️ P2SHAX8gCoZJxCXoAoKCf8Pr4oVqsqSxgjTDoW

Merkle Root

0f02b80f50d7b58d9280a6e68c783e8a2dae9d48dff4d795b069e4aaec81add7

Transactions (3)

Coinbase46831cc3ae7895…c93f974d4b856e

1 in → 1 out10.2900 XPM109 B

AX8gCoZJ…SxgjTDoW

d3b8a118e7a86d…af22106a1b6475

1 in → 3 out1.5800 XPM260 B

ANYfmupn…Ncap6MiM AZKDPwuc…J9BTHV94 AZVH8m73…FBqYw7C4

8f0401781b3443…e303500a24336f

1 in → 2 out0.6607 XPM226 B

AambVZEW…iwmZcAWt AH3vj8Mr…Zh4arJbh

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.

4.476 × 10⁹⁷(98-digit number)

44766020345142227283…16152897066089674719

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

4.476 × 10⁹⁷(98-digit number)

44766020345142227283…16152897066089674719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.476 × 10⁹⁷(98-digit number)

44766020345142227283…16152897066089674721

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

8.953 × 10⁹⁷(98-digit number)

89532040690284454567…32305794132179349439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.953 × 10⁹⁷(98-digit number)

89532040690284454567…32305794132179349441

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

1.790 × 10⁹⁸(99-digit number)

17906408138056890913…64611588264358698879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.790 × 10⁹⁸(99-digit number)

17906408138056890913…64611588264358698881

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

3.581 × 10⁹⁸(99-digit number)

35812816276113781827…29223176528717397759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.581 × 10⁹⁸(99-digit number)

35812816276113781827…29223176528717397761

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

7.162 × 10⁹⁸(99-digit number)

71625632552227563654…58446353057434795519

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #183,856

Cookie Preferences