Block #1,550,836

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/21/2016, 8:06:40 AM · Difficulty 10.6492 · 5,274,631 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9986ef9a26533694a0671ac37250d8e8d3fe72f3605b9201f474e77d60407ee2

View on Chainz ↗

Height

#1,550,836

Difficulty

10.649152

Transactions

Size

866 B

Version

Bits

0aa62ed6

Nonce

99,942,012

Timestamp

4/21/2016, 8:06:40 AM

Confirmations

5,274,631

Mined by

⛏️ P2SHASTTfMi4uU1ZPQjt7Y4yS7y5zxmZ7iNLuk

Merkle Root

a77a7b75e5a42406dc58b815a2e418c2bdaecf435d9e5d0bd3aa12ce3e2ea6c7

Transactions (2)

Coinbase40fe1037df57c9…fb89483318d664

1 in → 1 out8.8100 XPM110 B

ASTTfMi4…mZ7iNLuk

eadea9562c63bd…e7c97f262a4309

1 in → 15 out129.2162 XPM667 B

ALuJFPvW…o3Rpygyu AMQvxBuX…wTpqo2Na ALb74pZx…rXHYZe83 AKxkmYTj…JumnxJFz AMuEYzSo…Gmd5PTKP

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.

5.376 × 10⁹¹(92-digit number)

53769468893154680458…69248548141673532399

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

5.376 × 10⁹¹(92-digit number)

53769468893154680458…69248548141673532399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.376 × 10⁹¹(92-digit number)

53769468893154680458…69248548141673532401

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

1.075 × 10⁹²(93-digit number)

10753893778630936091…38497096283347064799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.075 × 10⁹²(93-digit number)

10753893778630936091…38497096283347064801

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

2.150 × 10⁹²(93-digit number)

21507787557261872183…76994192566694129599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.150 × 10⁹²(93-digit number)

21507787557261872183…76994192566694129601

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

4.301 × 10⁹²(93-digit number)

43015575114523744366…53988385133388259199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.301 × 10⁹²(93-digit number)

43015575114523744366…53988385133388259201

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

8.603 × 10⁹²(93-digit number)

86031150229047488732…07976770266776518399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.603 × 10⁹²(93-digit number)

86031150229047488732…07976770266776518401

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 #1,550,836

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