Block #273,679

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/25/2013, 10:28:56 PM · Difficulty 9.9554 · 6,543,129 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a41953ecb66ad1e4079c2996e9b35c8653deb36be6094e933bb34a509b926506

View on Chainz ↗

Height

#273,679

Difficulty

9.955399

Transactions

Size

904 B

Version

Bits

09f49501

Nonce

18,368

Timestamp

11/25/2013, 10:28:56 PM

Confirmations

6,543,129

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

7774d979589ce856aeac9d821cb51ba106807e7f7bb2c1eca4881b80212eef9f

Transactions (2)

Coinbase5a0a9b7c033fcd…dd137cdf7d2d1c

1 in → 2 out10.0800 XPM140 B

AKcbk49N…GJbKa7j1 ASNt3cJa…L5zCqAYM

f792cfa8f4a4fe…d474e652e865b4

4 in → 2 out10.0345 XPM670 B

AJhgf59P…W42GoeAR AVvAcrKQ…wWdybkGC

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.

1.571 × 10¹⁰⁵(106-digit number)

15718138436630639760…23003553459718415359

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

1.571 × 10¹⁰⁵(106-digit number)

15718138436630639760…23003553459718415359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.571 × 10¹⁰⁵(106-digit number)

15718138436630639760…23003553459718415361

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

3.143 × 10¹⁰⁵(106-digit number)

31436276873261279520…46007106919436830719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.143 × 10¹⁰⁵(106-digit number)

31436276873261279520…46007106919436830721

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

6.287 × 10¹⁰⁵(106-digit number)

62872553746522559040…92014213838873661439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.287 × 10¹⁰⁵(106-digit number)

62872553746522559040…92014213838873661441

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

1.257 × 10¹⁰⁶(107-digit number)

12574510749304511808…84028427677747322879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.257 × 10¹⁰⁶(107-digit number)

12574510749304511808…84028427677747322881

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

2.514 × 10¹⁰⁶(107-digit number)

25149021498609023616…68056855355494645759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.514 × 10¹⁰⁶(107-digit number)

25149021498609023616…68056855355494645761

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

Block #273,679

Cookie Preferences