Block #476,416

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/5/2014, 8:05:15 PM · Difficulty 10.4709 · 6,329,832 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e2b2ff0e425b9df946c4b3e550c06a5a41b95b877d794ef1552aa85bb6e202a9

View on Chainz ↗

Height

#476,416

Difficulty

10.470943

Transactions

Size

800 B

Version

Bits

0a788fbf

Nonce

249,246

Timestamp

4/5/2014, 8:05:15 PM

Confirmations

6,329,832

Mined by

⛏️ EaS@aATKK7iFzxU98qfet38JZnUDJ7swZm46KN1

Merkle Root

3eb5b71b9eef06e3cb931d203c1a1f25ae151e99e3181c378731efbaeee866c7

Transactions (1)

Coinbase3eb5b71b9eef06…31efbaeee866c7

1 in → 19 out9.1100 XPM709 B

ATKK7iFz…wZm46KN1 AQvZBsUo…hppgRZTJ ALqxX1WA…hsKjbnXn ANNg88pG…ppn21sTe AQyr8Lw3…hs4nt3Pn

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.

1.371 × 10⁹⁶(97-digit number)

13712723258618710484…90479018909206719999

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

1.371 × 10⁹⁶(97-digit number)

13712723258618710484…90479018909206719999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.371 × 10⁹⁶(97-digit number)

13712723258618710484…90479018909206720001

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

2.742 × 10⁹⁶(97-digit number)

27425446517237420969…80958037818413439999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.742 × 10⁹⁶(97-digit number)

27425446517237420969…80958037818413440001

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

5.485 × 10⁹⁶(97-digit number)

54850893034474841939…61916075636826879999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.485 × 10⁹⁶(97-digit number)

54850893034474841939…61916075636826880001

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

1.097 × 10⁹⁷(98-digit number)

10970178606894968387…23832151273653759999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.097 × 10⁹⁷(98-digit number)

10970178606894968387…23832151273653760001

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

2.194 × 10⁹⁷(98-digit number)

21940357213789936775…47664302547307519999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.194 × 10⁹⁷(98-digit number)

21940357213789936775…47664302547307520001

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 #476,416

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