Block #2,758,032

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 7/20/2018, 9:41:00 PM · Difficulty 11.6677 · 4,085,315 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c044bebf5105f99961cdca592d98d5387d5505e6d324c8b0bd6f9c98251ddb91

View on Chainz ↗

Height

#2,758,032

Difficulty

11.667738

Transactions

Size

845 B

Version

Bits

0baaf0e8

Nonce

282,157,413

Timestamp

7/20/2018, 9:41:00 PM

Confirmations

4,085,315

Mined by

⛏️ P2SHASMCk6GqM8KcgPnqXcnCdHtysBSpwLqucq

Merkle Root

b1bb47b65b58c5b1dc29479f9aec65a115e2946cf3d39924eafef4b03a09cab9

Transactions (3)

Coinbasede67b8b0b44205…0bc3f0a8ee3e13

1 in → 1 out7.3500 XPM110 B

ASMCk6Gq…SpwLqucq

7abc7431d4e0e9…47ba94ab49b78d

2 in → 2 out14.6900 XPM306 B

AdF2pfXL…CgxwH9Tg AWTAGcL4…jKZwu5r5

878cde7eaba2f2…4e66c4aadcad50

2 in → 2 out12.0300 XPM339 B

AM7HYByC…YhcyJvAq ATKYGWQU…cy1zpW8o

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.

1.036 × 10⁹⁴(95-digit number)

10367524760174419358…03900916850081249879

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

1.036 × 10⁹⁴(95-digit number)

10367524760174419358…03900916850081249879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.036 × 10⁹⁴(95-digit number)

10367524760174419358…03900916850081249881

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

2.073 × 10⁹⁴(95-digit number)

20735049520348838717…07801833700162499759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.073 × 10⁹⁴(95-digit number)

20735049520348838717…07801833700162499761

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

4.147 × 10⁹⁴(95-digit number)

41470099040697677434…15603667400324999519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.147 × 10⁹⁴(95-digit number)

41470099040697677434…15603667400324999521

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

8.294 × 10⁹⁴(95-digit number)

82940198081395354869…31207334800649999039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.294 × 10⁹⁴(95-digit number)

82940198081395354869…31207334800649999041

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

1.658 × 10⁹⁵(96-digit number)

16588039616279070973…62414669601299998079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.658 × 10⁹⁵(96-digit number)

16588039616279070973…62414669601299998081

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

3.317 × 10⁹⁵(96-digit number)

33176079232558141947…24829339202599996159

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 #2,758,032

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