Block #258,506

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/13/2013, 2:37:46 AM · Difficulty 9.9765 · 6,550,593 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6c0933106ce325e484c921bd47e9034acdd3f16f220b2de9dbf326add3533ccd

View on Chainz ↗

Height

#258,506

Difficulty

9.976464

Transactions

Size

57.40 KB

Version

Bits

09f9f990

Nonce

37,568

Timestamp

11/13/2013, 2:37:46 AM

Confirmations

6,550,593

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

7c8ade56e3b613881dea225412b432154485d46338f233ea42d89fd171caf4bc

Transactions (2)

Coinbase4cdb8b41a93055…a0f635577d50d5

1 in → 2 out10.6400 XPM141 B

AKcbk49N…GJbKa7j1 AHsw4d6U…EnM8UXNZ

feadae9bcc5ba5…34cc4a2afa29da

395 in → 2 out40.0100 XPM57.17 KB

AR9eeU4W…HNdvqTzE AMAPge2C…LqWrqyCz

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.

7.892 × 10⁹⁷(98-digit number)

78920246098498304490…65266551269879820799

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

7.892 × 10⁹⁷(98-digit number)

78920246098498304490…65266551269879820799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.892 × 10⁹⁷(98-digit number)

78920246098498304490…65266551269879820801

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

1.578 × 10⁹⁸(99-digit number)

15784049219699660898…30533102539759641599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.578 × 10⁹⁸(99-digit number)

15784049219699660898…30533102539759641601

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

3.156 × 10⁹⁸(99-digit number)

31568098439399321796…61066205079519283199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.156 × 10⁹⁸(99-digit number)

31568098439399321796…61066205079519283201

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

6.313 × 10⁹⁸(99-digit number)

63136196878798643592…22132410159038566399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.313 × 10⁹⁸(99-digit number)

63136196878798643592…22132410159038566401

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

1.262 × 10⁹⁹(100-digit number)

12627239375759728718…44264820318077132799

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 #258,506

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