Block #2,633,497

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/28/2018, 11:31:56 AM · Difficulty 11.1936 · 4,197,025 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9100a7e996cbf1337ee2f257047e42ef530207dc28d07723ee1a5185aed8e4fc

View on Chainz ↗

Height

#2,633,497

Difficulty

11.193593

Transactions

Size

1.47 KB

Version

Bits

0b318f48

Nonce

1,676,247,057

Timestamp

4/28/2018, 11:31:56 AM

Confirmations

4,197,025

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

30c11b4ce6e65a296107792ddeef5dea08caa2136111e841a76acbf5c28d6a23

Transactions (3)

Coinbasece0fe98a4f08c2…341484cd037d57

1 in → 1 out8.0000 XPM109 B

Adqah8zh…1WwoHJ9t

eee99364aa09db…83ef06d89de134

1 in → 1 out299.9900 XPM192 B

AQwQCJai…x2rDr9Lo

4ea34ad5b56da9…32466726927f6d

7 in → 2 out149.3224 XPM1.09 KB

AcgUjstD…7gCcBw7c AYkHP8Ch…XZWkALxV

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.

4.823 × 10⁹⁶(97-digit number)

48232244588041017072…53111133320399103999

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

4.823 × 10⁹⁶(97-digit number)

48232244588041017072…53111133320399103999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.823 × 10⁹⁶(97-digit number)

48232244588041017072…53111133320399104001

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

9.646 × 10⁹⁶(97-digit number)

96464489176082034144…06222266640798207999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.646 × 10⁹⁶(97-digit number)

96464489176082034144…06222266640798208001

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

1.929 × 10⁹⁷(98-digit number)

19292897835216406828…12444533281596415999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.929 × 10⁹⁷(98-digit number)

19292897835216406828…12444533281596416001

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

3.858 × 10⁹⁷(98-digit number)

38585795670432813657…24889066563192831999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.858 × 10⁹⁷(98-digit number)

38585795670432813657…24889066563192832001

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

7.717 × 10⁹⁷(98-digit number)

77171591340865627315…49778133126385663999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.717 × 10⁹⁷(98-digit number)

77171591340865627315…49778133126385664001

Verify on FactorDB ↗Wolfram Alpha ↗

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

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.543 × 10⁹⁸(99-digit number)

15434318268173125463…99556266252771327999

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #2,633,497

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