Block #272,739

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/25/2013, 10:24:39 AM · Difficulty 9.9534 · 6,538,117 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7bbd2d15842bf60acb7b5b82e8e158cdede61cdc967e818d66fe016d2a125ea3

View on Chainz ↗

Height

#272,739

Difficulty

9.953417

Transactions

Size

8.19 KB

Version

Bits

09f4132b

Nonce

5,024

Timestamp

11/25/2013, 10:24:39 AM

Confirmations

6,538,117

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

2dedb29e86b7ddda1aaffd9c14bd0a18b9cbfb49a0a64a81cf803f7fe043f717

Transactions (3)

Coinbase6c1a38039092a2…9b26614a7a7dd4

1 in → 2 out10.1800 XPM141 B

AKcbk49N…GJbKa7j1 ASNt3cJa…L5zCqAYM

9f8e7869c97895…0d7b4fc6b631fb

52 in → 2 out555.4328 XPM7.60 KB

AeEx4AUz…mfd24hgL Ac7RAQMV…nKWU2GLU

69117fc5072d82…e7e326b6cc1df1

2 in → 2 out14.7094 XPM374 B

AcqK8med…QMSSPa4h Acd8ns3R…z4tgg26P

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.

2.390 × 10¹⁰³(104-digit number)

23907920120189266433…66827349101571900159

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

2.390 × 10¹⁰³(104-digit number)

23907920120189266433…66827349101571900159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.390 × 10¹⁰³(104-digit number)

23907920120189266433…66827349101571900161

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

4.781 × 10¹⁰³(104-digit number)

47815840240378532867…33654698203143800319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.781 × 10¹⁰³(104-digit number)

47815840240378532867…33654698203143800321

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

9.563 × 10¹⁰³(104-digit number)

95631680480757065735…67309396406287600639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.563 × 10¹⁰³(104-digit number)

95631680480757065735…67309396406287600641

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

1.912 × 10¹⁰⁴(105-digit number)

19126336096151413147…34618792812575201279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.912 × 10¹⁰⁴(105-digit number)

19126336096151413147…34618792812575201281

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

3.825 × 10¹⁰⁴(105-digit number)

38252672192302826294…69237585625150402559

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

Block #272,739

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