Block #1,570,249

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/3/2016, 4:09:55 PM · Difficulty 10.7480 · 5,247,495 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

617975f465a8a1ebb095038d259be746647450f2911d9537c0eb7418522cc784

View on Chainz ↗

Height

#1,570,249

Difficulty

10.747988

Transactions

Size

1004 B

Version

Bits

0abf7c1e

Nonce

1,807,692,193

Timestamp

5/3/2016, 4:09:55 PM

Confirmations

5,247,495

Mined by

⛏️ P2SHAS5qepxNbQd9NdEDwA5ogfRMddjgqz3NVP

Merkle Root

3157ac989fe38a7b337d71651fd6f065b0c794e83d46079d9218f412e3f9cc2b

Transactions (2)

Coinbase08fb7def8eed84…93046638991ab9

1 in → 1 out8.6500 XPM109 B

AS5qepxN…jgqz3NVP

d96461acdba2d2…2ea40cbad1995a

1 in → 19 out146.0566 XPM803 B

ATn65h1d…dKBd9y2D Af5Gz1wp…evDx5GoB AKaz3dni…sbqBja51 AVi44k3u…zoKckoQW Ads92bAu…bPgeu2Eo

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.

4.018 × 10⁹⁸(99-digit number)

40185393181336102136…93013228306841599999

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

4.018 × 10⁹⁸(99-digit number)

40185393181336102136…93013228306841599999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.018 × 10⁹⁸(99-digit number)

40185393181336102136…93013228306841600001

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

8.037 × 10⁹⁸(99-digit number)

80370786362672204272…86026456613683199999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.037 × 10⁹⁸(99-digit number)

80370786362672204272…86026456613683200001

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

1.607 × 10⁹⁹(100-digit number)

16074157272534440854…72052913227366399999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.607 × 10⁹⁹(100-digit number)

16074157272534440854…72052913227366400001

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

3.214 × 10⁹⁹(100-digit number)

32148314545068881709…44105826454732799999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.214 × 10⁹⁹(100-digit number)

32148314545068881709…44105826454732800001

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

6.429 × 10⁹⁹(100-digit number)

64296629090137763418…88211652909465599999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.429 × 10⁹⁹(100-digit number)

64296629090137763418…88211652909465600001

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 #1,570,249

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