Block #398,659

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/10/2014, 9:24:39 PM · Difficulty 10.4241 · 6,428,050 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

17337298c60059618536ee913adb8257cdec06cc249d9781437f8a5062852152

View on Chainz ↗

Height

#398,659

Difficulty

10.424065

Transactions

Size

877 B

Version

Bits

0a6c8f8b

Nonce

35,395

Timestamp

2/10/2014, 9:24:39 PM

Confirmations

6,428,050

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

0e5e85c695a7d8f2e030508b8b2970216c98f2c5ea47d023cf47a3f59348714d

Transactions (2)

Coinbaseac1c7d1450a8cc…46a2c29a562a01

1 in → 1 out9.2000 XPM116 B

AbwWkWZt…kawDhufa

d2c109df592fb8…b2d2a357db26cd

4 in → 2 out1.1853 XPM669 B

AYUY6QBZ…nstBEWCQ AYb9323f…7f5sEBkS

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.

1.498 × 10¹⁰⁰(101-digit number)

14987634308038714799…48081556033476055039

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

1.498 × 10¹⁰⁰(101-digit number)

14987634308038714799…48081556033476055039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.498 × 10¹⁰⁰(101-digit number)

14987634308038714799…48081556033476055041

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

2.997 × 10¹⁰⁰(101-digit number)

29975268616077429598…96163112066952110079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.997 × 10¹⁰⁰(101-digit number)

29975268616077429598…96163112066952110081

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

5.995 × 10¹⁰⁰(101-digit number)

59950537232154859197…92326224133904220159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.995 × 10¹⁰⁰(101-digit number)

59950537232154859197…92326224133904220161

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

1.199 × 10¹⁰¹(102-digit number)

11990107446430971839…84652448267808440319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.199 × 10¹⁰¹(102-digit number)

11990107446430971839…84652448267808440321

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

2.398 × 10¹⁰¹(102-digit number)

23980214892861943678…69304896535616880639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.398 × 10¹⁰¹(102-digit number)

23980214892861943678…69304896535616880641

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 #398,659

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