Block #648,235

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 7/26/2014, 4:36:04 AM · Difficulty 10.9513 · 6,156,550 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5b3ad693c5bc3a9da1e87c3890ed9caae7dbf20bba95c84983833b8ab7d74af3

View on Chainz ↗

Height

#648,235

Difficulty

10.951314

Transactions

Size

468 B

Version

Bits

0af3894a

Nonce

131,686,723

Timestamp

7/26/2014, 4:36:04 AM

Confirmations

6,156,550

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

dd7188f2cbe2391e21e28870e199b79fa136ac49ba1c15a3decc46abe674e99c

Transactions (2)

Coinbaseef01533f5147ee…c9a6b2f11e425e

1 in → 1 out8.3300 XPM116 B

ANSXnLY2…Sd25TjkD

610f005401ddaf…86e9890f54de20

1 in → 4 out8.3100 XPM260 B

AeKNrjNj…1NEq95Ta AcNovFbg…sJ1oLH5E AcgLSLhU…uJ6co9oZ ASH3HaLZ…1LTAJLUm

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.

2.542 × 10⁹⁹(100-digit number)

25428948392213468019…88725599392032522239

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

2.542 × 10⁹⁹(100-digit number)

25428948392213468019…88725599392032522239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.542 × 10⁹⁹(100-digit number)

25428948392213468019…88725599392032522241

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

5.085 × 10⁹⁹(100-digit number)

50857896784426936039…77451198784065044479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.085 × 10⁹⁹(100-digit number)

50857896784426936039…77451198784065044481

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

1.017 × 10¹⁰⁰(101-digit number)

10171579356885387207…54902397568130088959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.017 × 10¹⁰⁰(101-digit number)

10171579356885387207…54902397568130088961

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

2.034 × 10¹⁰⁰(101-digit number)

20343158713770774415…09804795136260177919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.034 × 10¹⁰⁰(101-digit number)

20343158713770774415…09804795136260177921

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

4.068 × 10¹⁰⁰(101-digit number)

40686317427541548831…19609590272520355839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.068 × 10¹⁰⁰(101-digit number)

40686317427541548831…19609590272520355841

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