Block #2,653,336

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/8/2018, 8:00:48 AM · Difficulty 11.7379 · 4,180,663 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

62b8fa5fba8a89f755bc9d41e73d4836536897881d777ea5ce1926f671696e52

View on Chainz ↗

Height

#2,653,336

Difficulty

11.737876

Transactions

Size

1.72 KB

Version

Bits

0bbce571

Nonce

1,920,271,986

Timestamp

5/8/2018, 8:00:48 AM

Confirmations

4,180,663

Mined by

⛏️ P2SHAbkuLrnob83FUXYFrafjF1RLLEUJqUUPmS

Merkle Root

ea20184c46d48bdd04cee4b36027c00163cc348e7e8e44e30c508e5675e6f8d0

Transactions (4)

Coinbasedea3c16ae795f1…b8de48c3f3068d

1 in → 1 out7.2800 XPM110 B

AbkuLrno…UJqUUPmS

4c011353a92f00…50ece0c2f70579

2 in → 2 out5062.9700 XPM376 B

AYqZWCTX…cH3imj1H AbocCjzQ…iKL36pCV

8a107c088d2b21…ad055535c022f5

2 in → 2 out821.0425 XPM373 B

ALcdnLm8…xjzErnDz Ae7Bt4sx…JEouoTnV

d6bc8b553476be…45b8d4dd6420e8

5 in → 2 out225.0244 XPM815 B

AcWfSxMB…HarzPBLh AY8PErqK…gv7kMfQz

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.

8.739 × 10⁹⁶(97-digit number)

87390025055586621287…43352614499874991999

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

8.739 × 10⁹⁶(97-digit number)

87390025055586621287…43352614499874991999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.739 × 10⁹⁶(97-digit number)

87390025055586621287…43352614499874992001

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

1.747 × 10⁹⁷(98-digit number)

17478005011117324257…86705228999749983999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.747 × 10⁹⁷(98-digit number)

17478005011117324257…86705228999749984001

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

3.495 × 10⁹⁷(98-digit number)

34956010022234648515…73410457999499967999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.495 × 10⁹⁷(98-digit number)

34956010022234648515…73410457999499968001

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

6.991 × 10⁹⁷(98-digit number)

69912020044469297030…46820915998999935999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.991 × 10⁹⁷(98-digit number)

69912020044469297030…46820915998999936001

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

1.398 × 10⁹⁸(99-digit number)

13982404008893859406…93641831997999871999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.398 × 10⁹⁸(99-digit number)

13982404008893859406…93641831997999872001

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

2.796 × 10⁹⁸(99-digit number)

27964808017787718812…87283663995999743999

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 #2,653,336

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