Block #309,070

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/13/2013, 10:17:26 AM · Difficulty 9.9947 · 6,501,835 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1edb2e94683d6d6c3e8d2f103ed7893419684155697daa5f0101b217bbfd461c

View on Chainz ↗

Height

#309,070

Difficulty

9.994709

Transactions

Size

1.99 KB

Version

Bits

09fea546

Nonce

73,026

Timestamp

12/13/2013, 10:17:26 AM

Confirmations

6,501,835

Mined by

⛏️ NaRAZ2pPuKgN7GXPJPBLxtm9bkWcE95SN2Yr7

Merkle Root

19336bd5d6f873aec78cd8232005cce68c5382a1b8217f7c61c2776664f24184

Transactions (4)

Coinbase820942682dcf75…66a3ee352cc489

1 in → 28 out9.9800 XPM1015 B

AZ2pPuKg…95SN2Yr7 Aac9Hjdg…P4ktypc3 AG5YAjec…VhA4Aeh1 Ad9pSzHt…cpJ3y2zz AbtgNzNb…9Atvu81w

d4c5d0cb4ba42b…c5b4bd76fbebfe

2 in → 2 out10.2848 XPM374 B

AKc2zo7j…PxUhcLd3 AbR7Gnot…56Uxo8Q2

e35d45992549a0…649a7a5f14220d

2 in → 1 out1.9900 XPM339 B

AWFC8PLc…ifjNgpb4

ad66b5478322f7…579964d6130d81

1 in → 2 out4.6839 XPM226 B

AaBm1onG…yeeJ5wh8 AGsZPR2M…TohGhvj8

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.

2.024 × 10⁹⁰(91-digit number)

20245459069114217422…59490923749764696079

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

2.024 × 10⁹⁰(91-digit number)

20245459069114217422…59490923749764696079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.024 × 10⁹⁰(91-digit number)

20245459069114217422…59490923749764696081

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

4.049 × 10⁹⁰(91-digit number)

40490918138228434845…18981847499529392159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.049 × 10⁹⁰(91-digit number)

40490918138228434845…18981847499529392161

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

8.098 × 10⁹⁰(91-digit number)

80981836276456869690…37963694999058784319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.098 × 10⁹⁰(91-digit number)

80981836276456869690…37963694999058784321

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

1.619 × 10⁹¹(92-digit number)

16196367255291373938…75927389998117568639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.619 × 10⁹¹(92-digit number)

16196367255291373938…75927389998117568641

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

3.239 × 10⁹¹(92-digit number)

32392734510582747876…51854779996235137279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.239 × 10⁹¹(92-digit number)

32392734510582747876…51854779996235137281

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #309,070

Cookie Preferences