Block #248,800

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/7/2013, 2:25:41 PM · Difficulty 9.9661 · 6,578,434 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e9539c5c7995ea47065dd512390b6ad40cc133ecb3ee10c77b7ae975925dda85

View on Chainz ↗

Height

#248,800

Difficulty

9.966145

Transactions

Size

975 B

Version

Bits

09f75547

Nonce

9,984

Timestamp

11/7/2013, 2:25:41 PM

Confirmations

6,578,434

Mined by

⛏️ P2SHARmAMwyuAi8euPwQcDptyGopF9P7Kn74ZT

Merkle Root

56202043389776f603a7efcc1dec0e748b0c540c1fcc84f71d496917a5e7c990

Transactions (3)

Coinbase8c11313c65f9ac…ffaa288539e57f

1 in → 2 out10.0700 XPM137 B

ARmAMwyu…P7Kn74ZT AU6kq4CL…dQBLvxLp

3f9506c92cf0ac…955e74583a77e6

1 in → 2 out8.0398 XPM225 B

AcKJ6bnn…Xc5s5shh ANThwWTs…H7ZfDQZC

7808f24e9a66e4…8a58f14de9630d

3 in → 2 out2.0286 XPM523 B

Abyspbiu…iX9n961T AeiC6eHW…Tqn1kz8x

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.

2.220 × 10⁹⁴(95-digit number)

22208821638394363332…07348752540385798339

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

2.220 × 10⁹⁴(95-digit number)

22208821638394363332…07348752540385798339

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.220 × 10⁹⁴(95-digit number)

22208821638394363332…07348752540385798341

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

4.441 × 10⁹⁴(95-digit number)

44417643276788726664…14697505080771596679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.441 × 10⁹⁴(95-digit number)

44417643276788726664…14697505080771596681

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

8.883 × 10⁹⁴(95-digit number)

88835286553577453328…29395010161543193359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.883 × 10⁹⁴(95-digit number)

88835286553577453328…29395010161543193361

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

1.776 × 10⁹⁵(96-digit number)

17767057310715490665…58790020323086386719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.776 × 10⁹⁵(96-digit number)

17767057310715490665…58790020323086386721

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

3.553 × 10⁹⁵(96-digit number)

35534114621430981331…17580040646172773439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.553 × 10⁹⁵(96-digit number)

35534114621430981331…17580040646172773441

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 #248,800

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