Block #1,529,561

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/6/2016, 10:04:23 PM · Difficulty 10.6105 · 5,313,336 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b6939da8a415401b4f5f916050639e2c32f1410dc2f218fefd073af851c5448e

View on Chainz ↗

Height

#1,529,561

Difficulty

10.610548

Transactions

Size

1.65 KB

Version

Bits

0a9c4ce2

Nonce

1,045,669,522

Timestamp

4/6/2016, 10:04:23 PM

Confirmations

5,313,336

Mined by

⛏️ P2SHARMkgtCgVbaSoydsppAY81ncabs3aiJsjE

Merkle Root

bfd33142ce13bac91f520e32bd5b132560105b178025e23aaa32d6add2fe33f6

Transactions (2)

Coinbasef6a044b1f939f1…e2eceaab6709d9

1 in → 1 out8.8900 XPM110 B

ARMkgtCg…s3aiJsjE

623a22baa770fa…b1038153b30d89

1 in → 39 out188.5875 XPM1.45 KB

AdHh6jf6…V36nT3BC ANbWCt9P…KDNYBq9J AVjmAN96…vhqRfZTa AJuuwvi3…KtoT9Bhz ARRGiRGe…roKD1v2R

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.

1.264 × 10⁹⁴(95-digit number)

12641780911872959136…50622159576915960319

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

1.264 × 10⁹⁴(95-digit number)

12641780911872959136…50622159576915960319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.264 × 10⁹⁴(95-digit number)

12641780911872959136…50622159576915960321

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

2.528 × 10⁹⁴(95-digit number)

25283561823745918272…01244319153831920639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.528 × 10⁹⁴(95-digit number)

25283561823745918272…01244319153831920641

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

5.056 × 10⁹⁴(95-digit number)

50567123647491836544…02488638307663841279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.056 × 10⁹⁴(95-digit number)

50567123647491836544…02488638307663841281

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

1.011 × 10⁹⁵(96-digit number)

10113424729498367308…04977276615327682559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.011 × 10⁹⁵(96-digit number)

10113424729498367308…04977276615327682561

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

2.022 × 10⁹⁵(96-digit number)

20226849458996734617…09954553230655365119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.022 × 10⁹⁵(96-digit number)

20226849458996734617…09954553230655365121

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 #1,529,561

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