Block #272,976

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/25/2013, 1:43:03 PM · Difficulty 9.9538 · 6,530,342 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4c62112cd24d6285430779e2e964124083f58e4888ece72e8e360b9e2d1222f0

View on Chainz ↗

Height

#272,976

Difficulty

9.953783

Transactions

Size

73.07 KB

Version

Bits

09f42b1c

Nonce

15,601

Timestamp

11/25/2013, 1:43:03 PM

Confirmations

6,530,342

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

2fd92feffc216128b75f72bcd3a26c756c2fe086fb4cd557b02928b496ff7ea0

Transactions (3)

Coinbased921a355809d6b…192ba31c16b159

1 in → 2 out10.8400 XPM142 B

AKcbk49N…GJbKa7j1 AU6kq4CL…dQBLvxLp

3501ae06337a8f…4defa5cd4496a9

4 in → 2 out49.9113 XPM670 B

AK591PTL…SH6veZec AVsfYqK2…DAkB2orv

87004a8819594d…c9a79e973753d0

499 in → 2 out100.0100 XPM72.18 KB

AMpN8pLF…7TZxNeRf AGXaftDA…E2qxzYYM

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.

2.990 × 10¹⁰²(103-digit number)

29909103318620310306…22275373065129873839

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

2.990 × 10¹⁰²(103-digit number)

29909103318620310306…22275373065129873839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.990 × 10¹⁰²(103-digit number)

29909103318620310306…22275373065129873841

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

5.981 × 10¹⁰²(103-digit number)

59818206637240620612…44550746130259747679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.981 × 10¹⁰²(103-digit number)

59818206637240620612…44550746130259747681

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

1.196 × 10¹⁰³(104-digit number)

11963641327448124122…89101492260519495359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.196 × 10¹⁰³(104-digit number)

11963641327448124122…89101492260519495361

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

2.392 × 10¹⁰³(104-digit number)

23927282654896248244…78202984521038990719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.392 × 10¹⁰³(104-digit number)

23927282654896248244…78202984521038990721

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

4.785 × 10¹⁰³(104-digit number)

47854565309792496489…56405969042077981439

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