Home/Chain Registry/Block #313,767

Block #313,767

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/15/2013, 3:23:07 PM · Difficulty 10.0256 · 6,482,728 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1a31a2b2608114e58b6cd0a701c29dc65ff5a7ffc21b8b3fcaf3c8b4e2e0ef50

View on Chainz ↗

Height

#313,767

Difficulty

10.025560

Transactions

Size

2.62 KB

Version

Bits

0a068b20

Nonce

98,257

Timestamp

12/15/2013, 3:23:07 PM

Confirmations

6,482,728

Merkle Root

3b001ffd256bb4f22a2495fb0f835cc91e8846106456c79212f4939519581c67

Transactions (4)

Coinbaseea5b8b50738f54…99fba55cc6e01b

1 in → 25 out9.9300 XPM913 B

AYtDvcGs…VuAcA7m7 AbtgNzNb…9Atvu81w Aac9Hjdg…P4ktypc3 ANNg88pG…ppn21sTe ASWX42VM…XypQABkY

7fdb0bc2db6f6b…42d92bf2aad256

8 in → 1 out7.0000 XPM1.20 KB

AKbz7RfM…QhRq2n8q

83367e3f6282ea…0d528abf8bc56d

1 in → 2 out2.6122 XPM226 B

Adkyazpk…mHty4BRn ARTcaCVH…LMYVgsg5

a673a1efa95fad…9eff35b5e4bb9c

1 in → 2 out2.3439 XPM226 B

AcDKAHmJ…ZGLUf4rV Aeyo8qkj…w3jEQAZT

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.

5.684 × 10⁹²(93-digit number)

56844031040579505495…93697561160233198480

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

5.684 × 10⁹²(93-digit number)

56844031040579505495…93697561160233198479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.684 × 10⁹²(93-digit number)

56844031040579505495…93697561160233198481

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

1.136 × 10⁹³(94-digit number)

11368806208115901099…87395122320466396959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.136 × 10⁹³(94-digit number)

11368806208115901099…87395122320466396961

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

2.273 × 10⁹³(94-digit number)

22737612416231802198…74790244640932793919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.273 × 10⁹³(94-digit number)

22737612416231802198…74790244640932793921

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

4.547 × 10⁹³(94-digit number)

45475224832463604396…49580489281865587839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.547 × 10⁹³(94-digit number)

45475224832463604396…49580489281865587841

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

9.095 × 10⁹³(94-digit number)

90950449664927208793…99160978563731175679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.095 × 10⁹³(94-digit number)

90950449664927208793…99160978563731175681

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 313767

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 1a31a2b2608114e58b6cd0a701c29dc65ff5a7ffc21b8b3fcaf3c8b4e2e0ef50

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 #313,767 on Chainz ↗