Block #270,792

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/24/2013, 5:16:47 AM · Difficulty 9.9515 · 6,530,410 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5e5057d7c077baa3b6d4bcb30379af208a41c74503306fbe4c77d654ae65fc2f

View on Chainz ↗

Height

#270,792

Difficulty

9.951489

Transactions

Size

1.47 KB

Version

Bits

09f394c5

Nonce

69,527

Timestamp

11/24/2013, 5:16:47 AM

Confirmations

6,530,410

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

af8f2f90a617d92b6a4c0ff638af4bc8eaee939e43b486b0caf04a6f693b6f90

Transactions (4)

Coinbaseed6dc423e58982…79f4f27dbeb91a

1 in → 2 out10.1100 XPM142 B

AKcbk49N…GJbKa7j1 ASNt3cJa…L5zCqAYM

3098b51a8c61e3…0214e6a1fe524c

5 in → 2 out3.0657 XPM817 B

AUmf5cQQ…Az3sDDyn AeKNrjNj…1NEq95Ta

a0f5466232d93c…eef5c4f730d82b

1 in → 2 out7.9617 XPM226 B

AdeAKmXa…K3eDHqsd AREDjRid…1PJoWWcd

baa8ca39613be4…faff65b1e1a782

1 in → 2 out4.0092 XPM227 B

AGGmFJ8e…TMZucQPX AL1HmgCg…LvgUoeo2

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.

5.865 × 10¹⁰³(104-digit number)

58657798799268794786…65795508415364482399

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

5.865 × 10¹⁰³(104-digit number)

58657798799268794786…65795508415364482399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.865 × 10¹⁰³(104-digit number)

58657798799268794786…65795508415364482401

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

1.173 × 10¹⁰⁴(105-digit number)

11731559759853758957…31591016830728964799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.173 × 10¹⁰⁴(105-digit number)

11731559759853758957…31591016830728964801

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

2.346 × 10¹⁰⁴(105-digit number)

23463119519707517914…63182033661457929599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.346 × 10¹⁰⁴(105-digit number)

23463119519707517914…63182033661457929601

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

4.692 × 10¹⁰⁴(105-digit number)

46926239039415035828…26364067322915859199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.692 × 10¹⁰⁴(105-digit number)

46926239039415035828…26364067322915859201

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

9.385 × 10¹⁰⁴(105-digit number)

93852478078830071657…52728134645831718399

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