Block #294,910

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/5/2013, 3:45:58 AM · Difficulty 9.9912 · 6,546,577 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f8572f974acd30bb90a8167b541e4bd17fcd524c947f6c189a35c2201a3d7514

View on Chainz ↗

Height

#294,910

Difficulty

9.991177

Transactions

Size

1.05 KB

Version

Bits

09fdbdc3

Nonce

34,523

Timestamp

12/5/2013, 3:45:58 AM

Confirmations

6,546,577

Mined by

⛏️ aRATMdAEtZBPTHcq8rn3o7nckbQi5XS8JqJg

Merkle Root

b8f66aac0139a9d403dc8bef91106a3a337cd5d5fe381eb270a9c9df5ea519e6

Transactions (1)

Coinbaseb8f66aac0139a9…a9c9df5ea519e6

1 in → 27 out10.0000 XPM981 B

ATMdAEtZ…5XS8JqJg Ad7MbJr3…yWRXUUkm Acskt6D1…Db4ci1L8 AWhCUP2R…fgLoE9HA Ad9pSzHt…cpJ3y2zz

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.

8.755 × 10⁹⁴(95-digit number)

87552187369719620951…79450601542552913919

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

8.755 × 10⁹⁴(95-digit number)

87552187369719620951…79450601542552913919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.755 × 10⁹⁴(95-digit number)

87552187369719620951…79450601542552913921

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

1.751 × 10⁹⁵(96-digit number)

17510437473943924190…58901203085105827839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.751 × 10⁹⁵(96-digit number)

17510437473943924190…58901203085105827841

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

3.502 × 10⁹⁵(96-digit number)

35020874947887848380…17802406170211655679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.502 × 10⁹⁵(96-digit number)

35020874947887848380…17802406170211655681

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

7.004 × 10⁹⁵(96-digit number)

70041749895775696761…35604812340423311359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.004 × 10⁹⁵(96-digit number)

70041749895775696761…35604812340423311361

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

1.400 × 10⁹⁶(97-digit number)

14008349979155139352…71209624680846622719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.400 × 10⁹⁶(97-digit number)

14008349979155139352…71209624680846622721

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 #294,910

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