Block #77,003

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/22/2013, 6:04:33 AM · Difficulty 9.1394 · 6,714,497 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cca09e99eaa08df71c4fba603d8a339e2e393c81fdc725c7efe5f5dd7ef07e98

View on Chainz ↗

Height

#77,003

Difficulty

9.139426

Transactions

Size

577 B

Version

Bits

0923b16b

Nonce

215

Timestamp

7/22/2013, 6:04:33 AM

Confirmations

6,714,497

Merkle Root

fef92f85a407f5083871eb1fc8f72004795d8cb03b24eb990f49342580b772b4

Transactions (2)

Coinbase33299b09fefa05…c91d6fcbb872b1

1 in → 1 out11.9600 XPM110 B

AZbCvUQM…TkdtSNzu

af3bad04cd7d7f…4e76e44751cc41

2 in → 2 out17.1700 XPM373 B

AcJnSyvn…VijA5cNC AJkJDiHi…DkZpGJXv

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.

1.419 × 10¹⁰⁴(105-digit number)

14198445670261327640…65620399524269421959

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

1.419 × 10¹⁰⁴(105-digit number)

14198445670261327640…65620399524269421959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.419 × 10¹⁰⁴(105-digit number)

14198445670261327640…65620399524269421961

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

2.839 × 10¹⁰⁴(105-digit number)

28396891340522655280…31240799048538843919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.839 × 10¹⁰⁴(105-digit number)

28396891340522655280…31240799048538843921

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

5.679 × 10¹⁰⁴(105-digit number)

56793782681045310561…62481598097077687839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.679 × 10¹⁰⁴(105-digit number)

56793782681045310561…62481598097077687841

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

1.135 × 10¹⁰⁵(106-digit number)

11358756536209062112…24963196194155375679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.135 × 10¹⁰⁵(106-digit number)

11358756536209062112…24963196194155375681

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

2.271 × 10¹⁰⁵(106-digit number)

22717513072418124224…49926392388310751359

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