Block #309,668

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 12/13/2013, 5:13:09 PM · Difficulty 9.9949 · 6,515,025 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ef854d02a54c542ca4328082f033b9f22ef0a5fac10f8dd18b67324cc4d8bbf0

View on Chainz ↗

Height

#309,668

Difficulty

9.994914

Transactions

Size

878 B

Version

Bits

09feb2b2

Nonce

5,114

Timestamp

12/13/2013, 5:13:09 PM

Confirmations

6,515,025

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

804ffcc6e20404a67cac772b0528a200fb3157631cfe89fbb15105f8ecf037a6

Transactions (4)

Coinbase346ecc514cfe2d…e0ea08d818b050

1 in → 1 out10.0300 XPM110 B

AeKNrjNj…1NEq95Ta

f75aff513418b6…5149cfec0ad4a5

1 in → 2 out9.9900 XPM226 B

ATa2z4oV…3gBeqp7b AScQmVfc…w9ecLjbp

26418056cda7fd…031f153292f79e

1 in → 2 out8.9461 XPM226 B

AeyRoYhX…JTkXbtsD AUe4V3q3…oQXpBVsq

bb7e288d6dc04d…7f2e319abe3fe2

1 in → 2 out8.8942 XPM226 B

AJxsHzHV…y3bKEsPu AcvhDWKU…JA5mgi9d

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.

6.078 × 10⁹⁵(96-digit number)

60788858316510736084…76237837284627171839

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

6.078 × 10⁹⁵(96-digit number)

60788858316510736084…76237837284627171839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.078 × 10⁹⁵(96-digit number)

60788858316510736084…76237837284627171841

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

1.215 × 10⁹⁶(97-digit number)

12157771663302147216…52475674569254343679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.215 × 10⁹⁶(97-digit number)

12157771663302147216…52475674569254343681

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

2.431 × 10⁹⁶(97-digit number)

24315543326604294433…04951349138508687359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.431 × 10⁹⁶(97-digit number)

24315543326604294433…04951349138508687361

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

4.863 × 10⁹⁶(97-digit number)

48631086653208588867…09902698277017374719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.863 × 10⁹⁶(97-digit number)

48631086653208588867…09902698277017374721

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

9.726 × 10⁹⁶(97-digit number)

97262173306417177734…19805396554034749439

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 #309,668

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