Block #71,618

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/20/2013, 7:32:53 PM · Difficulty 8.9934 · 6,738,192 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8765c91b4abe9b893d3b0379191f7d36198ee7458ec0314f36397740613b7dce

View on Chainz ↗

Height

#71,618

Difficulty

8.993360

Transactions

Size

429 B

Version

Bits

08fe4cd1

Nonce

Timestamp

7/20/2013, 7:32:53 PM

Confirmations

6,738,192

Mined by

⛏️ P2SHAMRJBb3V94CDPb3SssTj1B2eiHZv15uY6D

Merkle Root

182549b39ae71ab46601270d2cf5976a0ed43d6373afe0567c09116cdb6889bc

Transactions (2)

Coinbase8adf5bdc8508fa…f80e97f7e3d77c

1 in → 1 out12.3600 XPM110 B

AMRJBb3V…Zv15uY6D

03ce89a64b7605…e98c662e6d9f90

1 in → 2 out11.4000 XPM227 B

AKzkA3Bn…sMf8H3mp ASx9EPcc…2yoYj4Tn

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.

1.594 × 10¹⁰⁰(101-digit number)

15948754391895646107…62942778218575835859

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

1.594 × 10¹⁰⁰(101-digit number)

15948754391895646107…62942778218575835859

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.594 × 10¹⁰⁰(101-digit number)

15948754391895646107…62942778218575835861

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

3.189 × 10¹⁰⁰(101-digit number)

31897508783791292215…25885556437151671719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.189 × 10¹⁰⁰(101-digit number)

31897508783791292215…25885556437151671721

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

6.379 × 10¹⁰⁰(101-digit number)

63795017567582584430…51771112874303343439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.379 × 10¹⁰⁰(101-digit number)

63795017567582584430…51771112874303343441

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

1.275 × 10¹⁰¹(102-digit number)

12759003513516516886…03542225748606686879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.275 × 10¹⁰¹(102-digit number)

12759003513516516886…03542225748606686881

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

2.551 × 10¹⁰¹(102-digit number)

25518007027033033772…07084451497213373759

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 #71,618

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