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Block #295,038

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 12/5/2013, 5:41:02 AM · Difficulty 9.9912 · 6,498,054 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bd3f7d4e516c1d8f97d92a5d67adff6f9460eaab00561d0668f62b620473f10e

View on Chainz ↗

Height

#295,038

Difficulty

9.991203

Transactions

Size

1.55 KB

Version

Bits

09fdbf78

Nonce

1,623

Timestamp

12/5/2013, 5:41:02 AM

Confirmations

6,498,054

Merkle Root

14b7a4fb1f10481d64b6aad27e84cc0000dd931f9730106e8a89a192c040523b

Transactions (4)

Coinbased3a1d0d28b94e0…53992ab51e6711

1 in → 1 out10.0300 XPM110 B

AeKNrjNj…1NEq95Ta

1469184b0f06d7…d225d4045cd7e1

2 in → 1 out24.0000 XPM339 B

AMS434LY…ySngY6w4

e141b441767aff…3dbbf1c8e7955f

5 in → 2 out350.9296 XPM820 B

ANhQb1fr…Rz4Uhn5r APfWzKoh…5andUeRF

ca25e1e7067c8f…21d7c0a2d21919

1 in → 2 out3.1098 XPM226 B

AZT9REnf…cyyjugxy AaKMDtHq…v9JcvNnP

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.

8.765 × 10⁹³(94-digit number)

87651950723029019935…18845165840459118080

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

8.765 × 10⁹³(94-digit number)

87651950723029019935…18845165840459118079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.765 × 10⁹³(94-digit number)

87651950723029019935…18845165840459118081

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

1.753 × 10⁹⁴(95-digit number)

17530390144605803987…37690331680918236159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.753 × 10⁹⁴(95-digit number)

17530390144605803987…37690331680918236161

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

3.506 × 10⁹⁴(95-digit number)

35060780289211607974…75380663361836472319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.506 × 10⁹⁴(95-digit number)

35060780289211607974…75380663361836472321

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

7.012 × 10⁹⁴(95-digit number)

70121560578423215948…50761326723672944639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.012 × 10⁹⁴(95-digit number)

70121560578423215948…50761326723672944641

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

1.402 × 10⁹⁵(96-digit number)

14024312115684643189…01522653447345889279

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

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 295038

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 bd3f7d4e516c1d8f97d92a5d67adff6f9460eaab00561d0668f62b620473f10e

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 #295,038 on Chainz ↗