Block #128,071

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/21/2013, 11:47:00 PM · Difficulty 9.7829 · 6,682,648 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8af4fb89e16e7837b92e3d8df35e277f1b1dbf36d4234683747a4263c86affb6

View on Chainz ↗

Height

#128,071

Difficulty

9.782923

Transactions

Size

1.34 KB

Version

Bits

09c86da4

Nonce

21,701

Timestamp

8/21/2013, 11:47:00 PM

Confirmations

6,682,648

Mined by

⛏️ P2SHAGgALVaNXir18ADsBz3fgfE74TK78c9tGj

Merkle Root

37e573e349fa5b5852a99ee4988251dbb97a554dcb2225ac56302ac07f613e74

Transactions (5)

Coinbase0742351ad5b52c…d01b8bb645bf1d

1 in → 1 out10.4700 XPM109 B

AGgALVaN…K78c9tGj

9b72944cf32a48…f02e6b9157d11a

3 in → 1 out389.3900 XPM490 B

AGS9sPdH…NrxyVbEG

1897318ca4cdb3…ef9d79720e7be5

1 in → 2 out8.2901 XPM226 B

AcmRjVSh…zLqLLy9r ANN8gjLH…8ToruqzW

9e482ee0322e85…9ccf65bb143a43

1 in → 2 out8.1245 XPM226 B

AS8S8gnv…VzeUQg4G APTdxvbD…uFYLzKj7

35e6f33b57f6c5…d9cd673bfcaec0

1 in → 2 out4.3203 XPM226 B

AQR5tjeF…pj8msmLZ AWHeAuaa…DxhnUX4T

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.

2.418 × 10¹⁰⁸(109-digit number)

24181450406371530864…24995214058178375659

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

2.418 × 10¹⁰⁸(109-digit number)

24181450406371530864…24995214058178375659

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.418 × 10¹⁰⁸(109-digit number)

24181450406371530864…24995214058178375661

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

4.836 × 10¹⁰⁸(109-digit number)

48362900812743061729…49990428116356751319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.836 × 10¹⁰⁸(109-digit number)

48362900812743061729…49990428116356751321

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

9.672 × 10¹⁰⁸(109-digit number)

96725801625486123459…99980856232713502639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.672 × 10¹⁰⁸(109-digit number)

96725801625486123459…99980856232713502641

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

1.934 × 10¹⁰⁹(110-digit number)

19345160325097224691…99961712465427005279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.934 × 10¹⁰⁹(110-digit number)

19345160325097224691…99961712465427005281

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

3.869 × 10¹⁰⁹(110-digit number)

38690320650194449383…99923424930854010559

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 #128,071

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