Block #280,056

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/28/2013, 1:36:00 PM · Difficulty 9.9735 · 6,526,211 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

329655c0fad262ce77d0d04dc88b29f05dc396555afb6c79fce243a6933f090d

View on Chainz ↗

Height

#280,056

Difficulty

9.973489

Transactions

Size

4.16 KB

Version

Bits

09f9368f

Nonce

1,149

Timestamp

11/28/2013, 1:36:00 PM

Confirmations

6,526,211

Mined by

⛏️ P2SHAYaTpnoDjg4iRHnzSs6AaFf5TqEJq25nUy

Merkle Root

c79ffa50b585f2970658a957e176fb179b8f091108aa5552f3b530642f71ef6b

Transactions (5)

Coinbase248581518b0404…a634a480df8a8f

1 in → 2 out10.1149 XPM142 B

AYaTpnoD…EJq25nUy AKNbfPoc…jfkpwAyL

dc98721714e7da…5c431c330b00bc

2 in → 2 out20.1100 XPM306 B

AKixw9JQ…Lz7nfTzj APrX2g4u…mfyGRgEm

c43fd85cf97b7a…72ab55b7d7206b

21 in → 1 out6.3000 XPM3.08 KB

AGs9JbPj…3VsVL3Lz

369ce09e44a4fa…80a8159bb3d675

1 in → 1 out0.6880 XPM193 B

AcWW5CQn…MoCmUpaX

0bab1bc1eba2a1…7fd12a1a11613c

2 in → 2 out50.9900 XPM374 B

AN7uvY7M…znMA6da3 ANePci9a…jsj24qyD

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.

2.072 × 10¹⁰²(103-digit number)

20722931194699501635…89757635579237752159

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

2.072 × 10¹⁰²(103-digit number)

20722931194699501635…89757635579237752159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.072 × 10¹⁰²(103-digit number)

20722931194699501635…89757635579237752161

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

4.144 × 10¹⁰²(103-digit number)

41445862389399003271…79515271158475504319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.144 × 10¹⁰²(103-digit number)

41445862389399003271…79515271158475504321

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

8.289 × 10¹⁰²(103-digit number)

82891724778798006542…59030542316951008639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.289 × 10¹⁰²(103-digit number)

82891724778798006542…59030542316951008641

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

1.657 × 10¹⁰³(104-digit number)

16578344955759601308…18061084633902017279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.657 × 10¹⁰³(104-digit number)

16578344955759601308…18061084633902017281

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

3.315 × 10¹⁰³(104-digit number)

33156689911519202617…36122169267804034559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.315 × 10¹⁰³(104-digit number)

33156689911519202617…36122169267804034561

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 #280,056

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