Block #153,319

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/6/2013, 10:11:25 PM · Difficulty 9.8634 · 6,642,346 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

244e052154989141e376be96943257f0cc2ff638c34df4cb89ef451fc789bb32

View on Chainz ↗

Height

#153,319

Difficulty

9.863429

Transactions

Size

717 B

Version

Bits

09dd09a8

Nonce

296,412

Timestamp

9/6/2013, 10:11:25 PM

Confirmations

6,642,346

Mined by

⛏️ P2SHAYkoKAQ4RDKGS7byjZXQArv3A5uuj8DeZs

Merkle Root

1c5acb7ee3784c647664ead3626390a74ca330c4b677ad5907a1ea6176934a52

Transactions (2)

Coinbase753b41ba1f2efe…3ce7fe6ba4d7e9

1 in → 1 out10.2700 XPM109 B

AYkoKAQ4…uuj8DeZs

b8146e295c1ce1…8d1eabf5220c9c

3 in → 2 out200.0102 XPM521 B

AcptgUHu…e4URzmPa AHoRNYmw…2jurfBKH

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.

4.696 × 10⁸⁷(88-digit number)

46960677942058293863…36133871844725240759

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

4.696 × 10⁸⁷(88-digit number)

46960677942058293863…36133871844725240759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.696 × 10⁸⁷(88-digit number)

46960677942058293863…36133871844725240761

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

9.392 × 10⁸⁷(88-digit number)

93921355884116587726…72267743689450481519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.392 × 10⁸⁷(88-digit number)

93921355884116587726…72267743689450481521

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

1.878 × 10⁸⁸(89-digit number)

18784271176823317545…44535487378900963039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.878 × 10⁸⁸(89-digit number)

18784271176823317545…44535487378900963041

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

3.756 × 10⁸⁸(89-digit number)

37568542353646635090…89070974757801926079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.756 × 10⁸⁸(89-digit number)

37568542353646635090…89070974757801926081

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

7.513 × 10⁸⁸(89-digit number)

75137084707293270181…78141949515603852159

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