Block #59,896

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/18/2013, 4:53:53 AM · Difficulty 8.9669 · 6,757,481 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

90e504a0ccd611280c2b25338f1339e403722e91c22c6fce7c7c99c226a068b4

View on Chainz ↗

Height

#59,896

Difficulty

8.966930

Transactions

Size

1.54 KB

Version

Bits

08f788b4

Nonce

Timestamp

7/18/2013, 4:53:53 AM

Confirmations

6,757,481

Mined by

⛏️ P2SHAMXUMVrzuyPkuHeW8HFjSZnPsHRqbgiPK6

Merkle Root

710787e134f1412231e4a6423f367a8ae9170a9b0f6dfae915f555eb8377c678

Transactions (2)

Coinbase1a5280c62fa13e…8f7236c3bc2254

1 in → 1 out12.4400 XPM110 B

AMXUMVrz…RqbgiPK6

82a16e6ab26b2a…9821e6bddabad8

9 in → 1 out900.0000 XPM1.35 KB

ALNFWEQU…xsZZYXBi

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.

1.287 × 10¹⁰⁰(101-digit number)

12878213990148878499…71663762131642557599

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

1.287 × 10¹⁰⁰(101-digit number)

12878213990148878499…71663762131642557599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.287 × 10¹⁰⁰(101-digit number)

12878213990148878499…71663762131642557601

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

2.575 × 10¹⁰⁰(101-digit number)

25756427980297756998…43327524263285115199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.575 × 10¹⁰⁰(101-digit number)

25756427980297756998…43327524263285115201

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

5.151 × 10¹⁰⁰(101-digit number)

51512855960595513996…86655048526570230399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.151 × 10¹⁰⁰(101-digit number)

51512855960595513996…86655048526570230401

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

1.030 × 10¹⁰¹(102-digit number)

10302571192119102799…73310097053140460799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.030 × 10¹⁰¹(102-digit number)

10302571192119102799…73310097053140460801

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 8 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 8

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 #59,896

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