Block #75,477

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/21/2013, 4:42:21 PM · Difficulty 9.0081 · 6,715,748 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e8f0a4bad6408f3331c399e12c40ae23afd7b1d3ada207e4a548b5467ac1d7d8

View on Chainz ↗

Height

#75,477

Difficulty

9.008102

Transactions

Size

920 B

Version

Bits

090212f5

Nonce

1,062

Timestamp

7/21/2013, 4:42:21 PM

Confirmations

6,715,748

Merkle Root

81cbebb4b83bb24262c56ca7cf2b51c2d856af4f0424c9ec8608c33d27e62af1

Transactions (3)

Coinbase0d5df2961f310b…252bd0c999f4d9

1 in → 1 out12.3300 XPM110 B

AQUZLYww…W65MgAU5

24111de23d280b…b49deb8d87287a

3 in → 1 out239.9000 XPM488 B

AWgLSjbC…8aJ5fgEn

864fbd3ed3e2d4…6cf50fdcb0fe6b

1 in → 2 out43.7200 XPM227 B

AXjrKGdw…rDCRkYsC ANcWjKHM…BiUAz8C5

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.

3.100 × 10¹⁰⁶(107-digit number)

31006158276761462747…11106124708257120049

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

3.100 × 10¹⁰⁶(107-digit number)

31006158276761462747…11106124708257120049

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.100 × 10¹⁰⁶(107-digit number)

31006158276761462747…11106124708257120051

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

6.201 × 10¹⁰⁶(107-digit number)

62012316553522925494…22212249416514240099

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.201 × 10¹⁰⁶(107-digit number)

62012316553522925494…22212249416514240101

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

1.240 × 10¹⁰⁷(108-digit number)

12402463310704585098…44424498833028480199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.240 × 10¹⁰⁷(108-digit number)

12402463310704585098…44424498833028480201

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

2.480 × 10¹⁰⁷(108-digit number)

24804926621409170197…88848997666056960399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.480 × 10¹⁰⁷(108-digit number)

24804926621409170197…88848997666056960401

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

4.960 × 10¹⁰⁷(108-digit number)

49609853242818340395…77697995332113920799

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