Block #278,315

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/27/2013, 10:38:58 PM · Difficulty 9.9686 · 6,513,209 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

975104f9abf01cc27417ed2288d348d947af015b838bd5bbaff8151d9de067e3

View on Chainz ↗

Height

#278,315

Difficulty

9.968593

Transactions

Size

1.43 KB

Version

Bits

09f7f5b6

Nonce

5,722

Timestamp

11/27/2013, 10:38:58 PM

Confirmations

6,513,209

Merkle Root

2ef240ab940528221dfc28ab56d4de7af3de3e0c1f24a4487fd526d40ca05f9d

Transactions (4)

Coinbase48e878bb9311e6…410e21c3875296

1 in → 2 out10.0800 XPM140 B

AKcbk49N…GJbKa7j1 ASNt3cJa…L5zCqAYM

1ce95df6b2fb34…2a423515336399

3 in → 2 out50.0850 XPM521 B

AbUfJvC9…wfszQvqf ANkHGhCJ…hhnCkr7s

fe60e1375bfed4…a8ac25c4b35d70

3 in → 2 out100.0110 XPM521 B

AR29Rewc…EpVxNEvc AXfJYKVn…QktpQC8p

b9c1bcbdb187c5…563e1625d3f017

1 in → 1 out9.9915 XPM192 B

AdMZ1ADb…uPJfsx2W

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.

4.465 × 10¹⁰²(103-digit number)

44650128600839707515…66108621334354307889

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

4.465 × 10¹⁰²(103-digit number)

44650128600839707515…66108621334354307889

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.465 × 10¹⁰²(103-digit number)

44650128600839707515…66108621334354307891

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

8.930 × 10¹⁰²(103-digit number)

89300257201679415030…32217242668708615779

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.930 × 10¹⁰²(103-digit number)

89300257201679415030…32217242668708615781

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

1.786 × 10¹⁰³(104-digit number)

17860051440335883006…64434485337417231559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.786 × 10¹⁰³(104-digit number)

17860051440335883006…64434485337417231561

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

3.572 × 10¹⁰³(104-digit number)

35720102880671766012…28868970674834463119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.572 × 10¹⁰³(104-digit number)

35720102880671766012…28868970674834463121

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

7.144 × 10¹⁰³(104-digit number)

71440205761343532024…57737941349668926239

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