Block #279,960

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/28/2013, 12:47:24 PM · Difficulty 9.9732 · 6,518,488 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d563fc64719e9c26abb3f79c9ac94bcddeb4028cd71eea682b97dc9d4627a67c

View on Chainz ↗

Height

#279,960

Difficulty

9.973231

Transactions

Size

3.78 KB

Version

Bits

09f925b0

Nonce

1,707

Timestamp

11/28/2013, 12:47:24 PM

Confirmations

6,518,488

Mined by

⛏️ P2SHAYaTpnoDjg4iRHnzSs6AaFf5TqEJq25nUy

Merkle Root

66852159e25f9a2d9db75acaa5533f3b0a248957fa4596512ed85341f73f8668

Transactions (3)

Coinbase7b5b32ac0f6cc1…d81676c41a7c38

1 in → 2 out10.0900 XPM141 B

AYaTpnoD…EJq25nUy ASNt3cJa…L5zCqAYM

fc19972fe899ae…60e918452e6edf

2 in → 1 out1895.7160 XPM342 B

AWxATbnj…NbUyPYHc

865c1499d29567…4742ac42c10a7f

22 in → 1 out74.6120 XPM3.22 KB

AVRMcj9i…g1ZWRina

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.

4.557 × 10¹⁰⁰(101-digit number)

45571761958475983891…10852360014699643519

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

4.557 × 10¹⁰⁰(101-digit number)

45571761958475983891…10852360014699643519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.557 × 10¹⁰⁰(101-digit number)

45571761958475983891…10852360014699643521

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

9.114 × 10¹⁰⁰(101-digit number)

91143523916951967782…21704720029399287039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.114 × 10¹⁰⁰(101-digit number)

91143523916951967782…21704720029399287041

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

1.822 × 10¹⁰¹(102-digit number)

18228704783390393556…43409440058798574079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.822 × 10¹⁰¹(102-digit number)

18228704783390393556…43409440058798574081

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

3.645 × 10¹⁰¹(102-digit number)

36457409566780787113…86818880117597148159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.645 × 10¹⁰¹(102-digit number)

36457409566780787113…86818880117597148161

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

7.291 × 10¹⁰¹(102-digit number)

72914819133561574226…73637760235194296319

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