Block #289,827

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/2/2013, 9:39:52 AM · Difficulty 9.9888 · 6,520,302 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

becc9c049ab93de7412f59418dc25373503dde222fecfd0febc30bc376a3a16a

View on Chainz ↗

Height

#289,827

Difficulty

9.988803

Transactions

Size

1.08 KB

Version

Bits

09fd2230

Nonce

7,331

Timestamp

12/2/2013, 9:39:52 AM

Confirmations

6,520,302

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

31c51c0a1adf988ee9d854b61fe49c4ec5155415014578090119aaab298b2aca

Transactions (5)

Coinbase8c361a1f21d4d7…8c640b708461cf

1 in → 1 out10.0500 XPM110 B

AeKNrjNj…1NEq95Ta

66e715a336e86a…101218dd1ddfa2

1 in → 2 out5.7435 XPM226 B

APtwcBWH…VHwnTJge AScpdxtR…yPZg2qBD

cd1a995128b58a…2d72daa6c51760

1 in → 2 out2.7516 XPM225 B

APesK5SC…jwJKsK8K AMdV1ssz…sXdhP4jq

f73ed1402f3c5f…69e36f11784431

1 in → 2 out3.8694 XPM227 B

ASb1CwwX…zYxGLhT7 Ad2XpcnB…uQBbVCx7

bb86485d4c7586…689390a389d96c

1 in → 2 out3.7727 XPM227 B

AFowkBLN…RS52nPHT AUSEvpgj…pEGkKLia

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.

1.740 × 10⁹⁶(97-digit number)

17405699866355911260…58426209136268554559

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

1.740 × 10⁹⁶(97-digit number)

17405699866355911260…58426209136268554559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.740 × 10⁹⁶(97-digit number)

17405699866355911260…58426209136268554561

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

3.481 × 10⁹⁶(97-digit number)

34811399732711822521…16852418272537109119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.481 × 10⁹⁶(97-digit number)

34811399732711822521…16852418272537109121

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

6.962 × 10⁹⁶(97-digit number)

69622799465423645043…33704836545074218239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.962 × 10⁹⁶(97-digit number)

69622799465423645043…33704836545074218241

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

1.392 × 10⁹⁷(98-digit number)

13924559893084729008…67409673090148436479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.392 × 10⁹⁷(98-digit number)

13924559893084729008…67409673090148436481

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

2.784 × 10⁹⁷(98-digit number)

27849119786169458017…34819346180296872959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.784 × 10⁹⁷(98-digit number)

27849119786169458017…34819346180296872961

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 #289,827

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