Block #290,584

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/2/2013, 6:36:26 PM · Difficulty 9.9893 · 6,518,751 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4a56485a7b36dceb3451b95346f91a0567910545d2174779845c8318d12104c6

View on Chainz ↗

Height

#290,584

Difficulty

9.989304

Transactions

Size

1.11 KB

Version

Bits

09fd430c

Nonce

4,353

Timestamp

12/2/2013, 6:36:26 PM

Confirmations

6,518,751

Mined by

⛏️ P2SHAYaTpnoDjg4iRHnzSs6AaFf5TqEJq25nUy

Merkle Root

b6d1fe5815ae68a73b34744805086abe9295a32ec8ae6d3f21b135fd774991a8

Transactions (2)

Coinbase6e3b1cdc59e41e…402930d8a2f601

1 in → 2 out10.0200 XPM140 B

AYaTpnoD…EJq25nUy AKNbfPoc…jfkpwAyL

e2ac78daf25639…a2d2bd13f9ac49

4 in → 13 out40.0700 XPM906 B

ARitzeAs…zBHrD3ss ALXni592…rFt26Kdr AVrD6maY…W77cdqzz AQiFTVc4…BHKGMxPa ATBhsxnq…i856gqcA

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.

2.567 × 10¹⁰²(103-digit number)

25678007835034227212…36495438188299632879

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

2.567 × 10¹⁰²(103-digit number)

25678007835034227212…36495438188299632879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.567 × 10¹⁰²(103-digit number)

25678007835034227212…36495438188299632881

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

5.135 × 10¹⁰²(103-digit number)

51356015670068454425…72990876376599265759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.135 × 10¹⁰²(103-digit number)

51356015670068454425…72990876376599265761

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

1.027 × 10¹⁰³(104-digit number)

10271203134013690885…45981752753198531519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.027 × 10¹⁰³(104-digit number)

10271203134013690885…45981752753198531521

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

2.054 × 10¹⁰³(104-digit number)

20542406268027381770…91963505506397063039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.054 × 10¹⁰³(104-digit number)

20542406268027381770…91963505506397063041

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

4.108 × 10¹⁰³(104-digit number)

41084812536054763540…83927011012794126079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.108 × 10¹⁰³(104-digit number)

41084812536054763540…83927011012794126081

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 #290,584

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