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Block #351,510

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/9/2014, 6:13:33 PM · Difficulty 10.2963 · 6,439,882 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2be7a5e8d4d09f4aeb930b29b77fc7684049e99699b12ae05eebe7e7ba23b8c5

View on Chainz ↗

Height

#351,510

Difficulty

10.296294

Transactions

Size

206 B

Version

Bits

0a4bd9e6

Nonce

13,354

Timestamp

1/9/2014, 6:13:33 PM

Confirmations

6,439,882

Merkle Root

3223d0c6ccf0a12cc6d38edf23b638dc0782c72782fd7f96839f3f68d899d5a7

Transactions (1)

Coinbase3223d0c6ccf0a1…9f3f68d899d5a7

1 in → 1 out9.4200 XPM116 B

AbwWkWZt…kawDhufa

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.

3.903 × 10⁹³(94-digit number)

39036724131937177263…28848888888438660520

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

3.903 × 10⁹³(94-digit number)

39036724131937177263…28848888888438660519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.903 × 10⁹³(94-digit number)

39036724131937177263…28848888888438660521

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

7.807 × 10⁹³(94-digit number)

78073448263874354526…57697777776877321039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.807 × 10⁹³(94-digit number)

78073448263874354526…57697777776877321041

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

1.561 × 10⁹⁴(95-digit number)

15614689652774870905…15395555553754642079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.561 × 10⁹⁴(95-digit number)

15614689652774870905…15395555553754642081

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

3.122 × 10⁹⁴(95-digit number)

31229379305549741810…30791111107509284159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.122 × 10⁹⁴(95-digit number)

31229379305549741810…30791111107509284161

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

6.245 × 10⁹⁴(95-digit number)

62458758611099483621…61582222215018568319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.245 × 10⁹⁴(95-digit number)

62458758611099483621…61582222215018568321

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 351510

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 2be7a5e8d4d09f4aeb930b29b77fc7684049e99699b12ae05eebe7e7ba23b8c5

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 #351,510 on Chainz ↗