Home/Chain Registry/Block #2,651,502

Block #2,651,502

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/6/2018, 8:55:09 PM · Difficulty 11.7514 · 4,192,551 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

55f172cb19dfea38987dd0694f3883a2d42fea4ff36c2acce636cf7375c0bf51

View on Chainz ↗

Height

#2,651,502

Difficulty

11.751375

Transactions

Size

201 B

Version

Bits

0bc05a15

Nonce

1,443,446,413

Timestamp

5/6/2018, 8:55:09 PM

Confirmations

4,192,551

Merkle Root

d9dd4799b39897d2373927e7f9a2a648749d76a92a9957e56e8f22f3d7b01876

Transactions (1)

Coinbased9dd4799b39897…8f22f3d7b01876

1 in → 1 out7.2300 XPM110 B

AMGbxQc2…JNtG9jcY

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.

9.836 × 10⁹⁷(98-digit number)

98367529671035222527…75046000342571417600

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

9.836 × 10⁹⁷(98-digit number)

98367529671035222527…75046000342571417599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.836 × 10⁹⁷(98-digit number)

98367529671035222527…75046000342571417601

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

1.967 × 10⁹⁸(99-digit number)

19673505934207044505…50092000685142835199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.967 × 10⁹⁸(99-digit number)

19673505934207044505…50092000685142835201

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

3.934 × 10⁹⁸(99-digit number)

39347011868414089011…00184001370285670399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.934 × 10⁹⁸(99-digit number)

39347011868414089011…00184001370285670401

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

7.869 × 10⁹⁸(99-digit number)

78694023736828178022…00368002740571340799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.869 × 10⁹⁸(99-digit number)

78694023736828178022…00368002740571340801

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

1.573 × 10⁹⁹(100-digit number)

15738804747365635604…00736005481142681599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.573 × 10⁹⁹(100-digit number)

15738804747365635604…00736005481142681601

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

3.147 × 10⁹⁹(100-digit number)

31477609494731271208…01472010962285363199

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

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 2651502

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 55f172cb19dfea38987dd0694f3883a2d42fea4ff36c2acce636cf7375c0bf51

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 #2,651,502 on Chainz ↗

Block #2,651,502

Cookie Preferences