Block #279,915

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/28/2013, 12:23:53 PM · Difficulty 9.9731 · 6,524,362 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a11facf4a702dcbb2780acca4b935f98beb7c21c8a1027ce1ab2885866549cfc

View on Chainz ↗

Height

#279,915

Difficulty

9.973125

Transactions

Size

5.71 KB

Version

Bits

09f91eb7

Nonce

9,197

Timestamp

11/28/2013, 12:23:53 PM

Confirmations

6,524,362

Mined by

⛏️ P2SHAYaTpnoDjg4iRHnzSs6AaFf5TqEJq25nUy

Merkle Root

09f5999856bc7e41a6d758a4e1c78e4a512630a87a5386c35a22034f2a9a72db

Transactions (5)

Coinbase32421bcbf3463c…ea0f7afd4847a4

1 in → 2 out10.1100 XPM142 B

AYaTpnoD…EJq25nUy Abiw8n3q…ZnZfgvQW

d7eae7ef9aeb85…868ad79b717f69

4 in → 2 out7.3625 XPM670 B

AKBRUi69…nN7rRkjk AWS72x5W…QXo8WbGJ

0ffa527001d6a6…c8a92737c6bedb

1 in → 2 out12.5300 XPM192 B

AdLUJJeg…rmCBi6bW AbHZM4d2…8YBLXYao

e73c782d709a85…63911394774e87

5 in → 2 out2.9448 XPM819 B

ALXkdhWX…moJqQMcL AeMs81ii…zLSiMSKD

a0fae2544a3d2b…1dc65372f48a13

26 in → 2 out9.4472 XPM3.84 KB

AQw2cabK…zdb5SVsG ARvYrhC6…Kjc3sCX6

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.

3.023 × 10¹⁰¹(102-digit number)

30234716096200341585…68357438099673838079

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

3.023 × 10¹⁰¹(102-digit number)

30234716096200341585…68357438099673838079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.023 × 10¹⁰¹(102-digit number)

30234716096200341585…68357438099673838081

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

6.046 × 10¹⁰¹(102-digit number)

60469432192400683171…36714876199347676159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.046 × 10¹⁰¹(102-digit number)

60469432192400683171…36714876199347676161

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

1.209 × 10¹⁰²(103-digit number)

12093886438480136634…73429752398695352319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.209 × 10¹⁰²(103-digit number)

12093886438480136634…73429752398695352321

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

2.418 × 10¹⁰²(103-digit number)

24187772876960273268…46859504797390704639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.418 × 10¹⁰²(103-digit number)

24187772876960273268…46859504797390704641

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

4.837 × 10¹⁰²(103-digit number)

48375545753920546536…93719009594781409279

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