Block #137,424

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/27/2013, 7:24:19 PM · Difficulty 9.8214 · 6,655,648 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a2b050110082fe2ab67a666320dcda6a9ae2a6fe1c02c0c45fc7a2e58ee0d8f4

View on Chainz ↗

Height

#137,424

Difficulty

9.821443

Transactions

Size

580 B

Version

Bits

09d24a1d

Nonce

33,783

Timestamp

8/27/2013, 7:24:19 PM

Confirmations

6,655,648

Merkle Root

b157177efd8490a0e6cd9e76d8d27396d5f676a0df81ca5b7a3ea782059e1dbe

Transactions (3)

Coinbase51012829d31260…933c1a911f3434

1 in → 1 out10.3700 XPM109 B

ARSMnghC…RHqqdAQJ

c994622d1d74cc…c0b1fd74b774e1

1 in → 1 out10.4200 XPM156 B

AQahrKpc…HpNmeomw

1f76ebfa68280b…8c8773fcf6d6c0

1 in → 2 out7.9234 XPM225 B

AXmTtqMm…vdhqnvN8 ANN8gjLH…8ToruqzW

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.

2.564 × 10⁹⁵(96-digit number)

25642210909023711408…40708173723688581319

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

2.564 × 10⁹⁵(96-digit number)

25642210909023711408…40708173723688581319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.564 × 10⁹⁵(96-digit number)

25642210909023711408…40708173723688581321

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

5.128 × 10⁹⁵(96-digit number)

51284421818047422817…81416347447377162639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.128 × 10⁹⁵(96-digit number)

51284421818047422817…81416347447377162641

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

1.025 × 10⁹⁶(97-digit number)

10256884363609484563…62832694894754325279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.025 × 10⁹⁶(97-digit number)

10256884363609484563…62832694894754325281

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

2.051 × 10⁹⁶(97-digit number)

20513768727218969127…25665389789508650559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.051 × 10⁹⁶(97-digit number)

20513768727218969127…25665389789508650561

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

4.102 × 10⁹⁶(97-digit number)

41027537454437938254…51330779579017301119

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