Block #1,508,154

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 3/22/2016, 10:11:09 PM · Difficulty 10.6235 · 5,299,054 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

41e519df79f0bd677b254e7a0b7028b62326331fb06335fe8db6bfb00a23316b

View on Chainz ↗

Height

#1,508,154

Difficulty

10.623523

Transactions

Size

83.56 KB

Version

Bits

0a9f9f36

Nonce

237,286,823

Timestamp

3/22/2016, 10:11:09 PM

Confirmations

5,299,054

Mined by

⛏️ P2SHAKspNrq1NxQLhpW7SVVDRiyr6UkPgRzbDW

Merkle Root

c3169b3e6fb5e99612970d6d0e46825f5dfd8adb9687c40845067ed728f3bc9f

Transactions (3)

Coinbase13ad772e686875…bd7c4956664b69

1 in → 1 out9.7100 XPM109 B

AKspNrq1…kPgRzbDW

2a6ffe02263dad…d2d55fce2f24ce

570 in → 1 out15.0000 XPM82.42 KB

AW9z6iyE…ZMok5rfx

67b82efdceb48c…8e87bc4871a249

1 in → 24 out175.9054 XPM975 B

APUT85mx…jDUpTyRu AQ3vWYn3…jTdcACHF ALvrh4nC…Vfv3w9nW ASPevCVM…PbZJuJQd ASf56EmJ…urQdVeD5

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.

9.062 × 10⁹³(94-digit number)

90623583404394445585…50319222784251933919

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

9.062 × 10⁹³(94-digit number)

90623583404394445585…50319222784251933919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.062 × 10⁹³(94-digit number)

90623583404394445585…50319222784251933921

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

1.812 × 10⁹⁴(95-digit number)

18124716680878889117…00638445568503867839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.812 × 10⁹⁴(95-digit number)

18124716680878889117…00638445568503867841

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

3.624 × 10⁹⁴(95-digit number)

36249433361757778234…01276891137007735679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.624 × 10⁹⁴(95-digit number)

36249433361757778234…01276891137007735681

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

7.249 × 10⁹⁴(95-digit number)

72498866723515556468…02553782274015471359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.249 × 10⁹⁴(95-digit number)

72498866723515556468…02553782274015471361

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

1.449 × 10⁹⁵(96-digit number)

14499773344703111293…05107564548030942719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.449 × 10⁹⁵(96-digit number)

14499773344703111293…05107564548030942721

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

2.899 × 10⁹⁵(96-digit number)

28999546689406222587…10215129096061885439

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 #1,508,154

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