Block #1,541,103

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/14/2016, 3:03:52 PM · Difficulty 10.6439 · 5,273,822 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

54427ef3a298c8e930da10f433b332ed587ebe0f2129ad88092ab3d78b4160c9

View on Chainz ↗

Height

#1,541,103

Difficulty

10.643925

Transactions

Size

969 B

Version

Bits

0aa4d84b

Nonce

1,450,709,073

Timestamp

4/14/2016, 3:03:52 PM

Confirmations

5,273,822

Mined by

⛏️ P2SHASpArQWqzwpnkY2ipwQ2U9afT9RK5uqHDT

Merkle Root

85b19eeb3ad13a5121b2154be0008f81c113ba326bbeedd972ae15f90f256f3e

Transactions (2)

Coinbase6ccf3e54836b2f…2029531973e20b

1 in → 1 out8.8200 XPM109 B

ASpArQWq…RK5uqHDT

c90bf40b1c780a…4c42f12809b10e

1 in → 18 out23.2018 XPM770 B

AZw67Mwn…VEGQ2bxR AQuzre4P…eRTZMMXk AZ2Dv6vs…YoKVyFme AYDJEEbg…1XpZ2X9u AVrnZ3dh…mAzgjZCS

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.

5.437 × 10⁹⁴(95-digit number)

54377655724463931963…05418282168414344359

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

5.437 × 10⁹⁴(95-digit number)

54377655724463931963…05418282168414344359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.437 × 10⁹⁴(95-digit number)

54377655724463931963…05418282168414344361

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

1.087 × 10⁹⁵(96-digit number)

10875531144892786392…10836564336828688719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.087 × 10⁹⁵(96-digit number)

10875531144892786392…10836564336828688721

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

2.175 × 10⁹⁵(96-digit number)

21751062289785572785…21673128673657377439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.175 × 10⁹⁵(96-digit number)

21751062289785572785…21673128673657377441

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

4.350 × 10⁹⁵(96-digit number)

43502124579571145570…43346257347314754879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.350 × 10⁹⁵(96-digit number)

43502124579571145570…43346257347314754881

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

8.700 × 10⁹⁵(96-digit number)

87004249159142291141…86692514694629509759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.700 × 10⁹⁵(96-digit number)

87004249159142291141…86692514694629509761

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 #1,541,103

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