Home/Chain Registry/Block #2,130,708

Block #2,130,708

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/24/2017, 2:39:43 PM · Difficulty 10.9100 · 4,710,966 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f4470f4458fcb4f8e7560ddda67a91089f4b697c9794485029e76eb4c52d60b6

View on Chainz ↗

Height

#2,130,708

Difficulty

10.909977

Transactions

Size

1.15 KB

Version

Bits

0ae8f442

Nonce

475,447,679

Timestamp

5/24/2017, 2:39:43 PM

Confirmations

4,710,966

Merkle Root

3d823f4293285df8a6442a9cc8ddb13e893a769fb32d4df0bc96823f387592a7

Transactions (4)

Coinbase03320e875c105e…0c495a2f07054a

1 in → 1 out8.4200 XPM110 B

AdhWr67H…Kx2jPZRe

be020ab5d117ab…37443ffa695732

3 in → 2 out1000.9450 XPM522 B

AVjkx5US…Kb9AKNAv AWapraWq…RFdjgZkt

7492f5b0baa0cd…dc32039c2d7daf

1 in → 2 out168410.2283 XPM226 B

ATjeKjRU…dEVNyPPF AJWMDJXd…4XY9YDRb

e52df533bfc377…2ffd644327a5b7

1 in → 2 out161396.0683 XPM226 B

AJPyWVrX…yTNpfAAg APphvYD5…ytChtGia

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.

4.450 × 10⁹⁷(98-digit number)

44509161915822922348…01474978602994319360

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

4.450 × 10⁹⁷(98-digit number)

44509161915822922348…01474978602994319359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.450 × 10⁹⁷(98-digit number)

44509161915822922348…01474978602994319361

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

8.901 × 10⁹⁷(98-digit number)

89018323831645844697…02949957205988638719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.901 × 10⁹⁷(98-digit number)

89018323831645844697…02949957205988638721

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

1.780 × 10⁹⁸(99-digit number)

17803664766329168939…05899914411977277439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.780 × 10⁹⁸(99-digit number)

17803664766329168939…05899914411977277441

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

3.560 × 10⁹⁸(99-digit number)

35607329532658337879…11799828823954554879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.560 × 10⁹⁸(99-digit number)

35607329532658337879…11799828823954554881

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

7.121 × 10⁹⁸(99-digit number)

71214659065316675758…23599657647909109759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.121 × 10⁹⁸(99-digit number)

71214659065316675758…23599657647909109761

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 2130708

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 f4470f4458fcb4f8e7560ddda67a91089f4b697c9794485029e76eb4c52d60b6

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 #2,130,708 on Chainz ↗

Block #2,130,708

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