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Block #1,588,788

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/17/2016, 4:24:46 PM · Difficulty 10.6519 · 5,244,097 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

12562c1e02068f751e048506980e79d63483aeee9e0cd2354123f7574c612d5f

View on Chainz ↗

Height

#1,588,788

Difficulty

10.651853

Transactions

Size

868 B

Version

Bits

0aa6dfd4

Nonce

57,173,755

Timestamp

5/17/2016, 4:24:46 PM

Confirmations

5,244,097

Merkle Root

4c1e4ff814e5d0891e69dc852f78e72fc65dabac0ac5812c7be4ccaa82b2316e

Transactions (2)

Coinbase3f24f469bd62e3…2c0a6e20524f72

1 in → 1 out8.8200 XPM109 B

AWA9bveg…TVP7k8Q3

9a568b3785d574…f618033d2c2ba2

4 in → 2 out0.3100 XPM669 B

AWnZxLBm…soimpFGL Aa38nf1h…kzkWbjCU

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.

6.910 × 10⁹⁴(95-digit number)

69100088462537330081…88510801182015052800

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

6.910 × 10⁹⁴(95-digit number)

69100088462537330081…88510801182015052799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.910 × 10⁹⁴(95-digit number)

69100088462537330081…88510801182015052801

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

1.382 × 10⁹⁵(96-digit number)

13820017692507466016…77021602364030105599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.382 × 10⁹⁵(96-digit number)

13820017692507466016…77021602364030105601

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

2.764 × 10⁹⁵(96-digit number)

27640035385014932032…54043204728060211199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.764 × 10⁹⁵(96-digit number)

27640035385014932032…54043204728060211201

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

5.528 × 10⁹⁵(96-digit number)

55280070770029864064…08086409456120422399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.528 × 10⁹⁵(96-digit number)

55280070770029864064…08086409456120422401

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

1.105 × 10⁹⁶(97-digit number)

11056014154005972812…16172818912240844799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.105 × 10⁹⁶(97-digit number)

11056014154005972812…16172818912240844801

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.

View full Prime Chain Discovery page →

★★☆☆☆

Rarity

UncommonChain length 10

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

Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height

getblockhash 1588788

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data

getblock 12562c1e02068f751e048506980e79d63483aeee9e0cd2354123f7574c612d5f

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help → Debug Window → Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #1,588,788 on Chainz ↗

Block #1,588,788

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