Block #87,073

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/28/2013, 3:01:39 PM · Difficulty 9.2808 · 6,718,602 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f840caa4203bdb91bd5540bec59b5c94150b466095c38d59ab4471c4e47cdbe3

View on Chainz ↗

Height

#87,073

Difficulty

9.280803

Transactions

Size

6.02 KB

Version

Bits

0947e2b3

Nonce

50,574

Timestamp

7/28/2013, 3:01:39 PM

Confirmations

6,718,602

Mined by

⛏️ P2SHATe7tG7XMJeCcfKBVw1awGupC6yczDSDEp

Merkle Root

1ea88502b22c86bd248685bb8d2d50defc7e8dbf485033a5d86830eccefc3738

Transactions (2)

Coinbasedfff4d8afbe22d…a198968d0c0480

1 in → 1 out11.6500 XPM109 B

ATe7tG7X…yczDSDEp

8fad712c4f8ad3…7a9aa4d2106590

51 in → 2 out572.8200 XPM5.82 KB

AVpW62a9…5PsHTFbw AGfz3APU…kNJNtgfb

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.

6.581 × 10¹⁰⁸(109-digit number)

65811929888144959995…25898393884083348489

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

6.581 × 10¹⁰⁸(109-digit number)

65811929888144959995…25898393884083348489

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.581 × 10¹⁰⁸(109-digit number)

65811929888144959995…25898393884083348491

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

1.316 × 10¹⁰⁹(110-digit number)

13162385977628991999…51796787768166696979

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.316 × 10¹⁰⁹(110-digit number)

13162385977628991999…51796787768166696981

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

2.632 × 10¹⁰⁹(110-digit number)

26324771955257983998…03593575536333393959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.632 × 10¹⁰⁹(110-digit number)

26324771955257983998…03593575536333393961

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

5.264 × 10¹⁰⁹(110-digit number)

52649543910515967996…07187151072666787919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.264 × 10¹⁰⁹(110-digit number)

52649543910515967996…07187151072666787921

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

1.052 × 10¹¹⁰(111-digit number)

10529908782103193599…14374302145333575839

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