Home/Chain Registry/Block #391,114

Block #391,114

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/5/2014, 2:43:26 PM · Difficulty 10.4281 · 6,425,755 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fe4b62de80b325f7738fa0676e89b0c48261efb358819842cca43c2023cbe52f

View on Chainz ↗

Height

#391,114

Difficulty

10.428144

Transactions

Size

1.54 KB

Version

Bits

0a6d9ad8

Nonce

43,519

Timestamp

2/5/2014, 2:43:26 PM

Confirmations

6,425,755

Merkle Root

fb913512089c8ff083e2981dfc89ef603ea31a0aec20f677454ce03344b21bc3

Transactions (4)

Coinbasea0393f31b53d7a…d442f5b6522b5b

1 in → 22 out9.1800 XPM811 B

AQvZBsUo…hppgRZTJ ALqxX1WA…hsKjbnXn Aac9Hjdg…P4ktypc3 AZV4TwxQ…8JnQqSoH AJLB8H7s…MRD4s5wA

c3c54b844e4e42…58d71a3eef6b67

1 in → 2 out9.2000 XPM225 B

AQCjQb3a…vepHuYZn ASTUCLVu…6cvYwkWv

29e4bb2d76afa3…2b74a48b5fdb00

1 in → 2 out9.2000 XPM226 B

AJ7wHRpG…pDpRoN7N AMSyWHBH…At7nVmCT

b6ec44c8e1c425…1433d0004ae4f2

1 in → 2 out9.2000 XPM226 B

AM4ZRoLQ…3oHiL3Jb AR9tDYoD…2cgTQBcU

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.

6.817 × 10⁹⁵(96-digit number)

68170404006916653122…76986305191598617600

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

6.817 × 10⁹⁵(96-digit number)

68170404006916653122…76986305191598617599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.817 × 10⁹⁵(96-digit number)

68170404006916653122…76986305191598617601

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

1.363 × 10⁹⁶(97-digit number)

13634080801383330624…53972610383197235199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.363 × 10⁹⁶(97-digit number)

13634080801383330624…53972610383197235201

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

2.726 × 10⁹⁶(97-digit number)

27268161602766661249…07945220766394470399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.726 × 10⁹⁶(97-digit number)

27268161602766661249…07945220766394470401

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

5.453 × 10⁹⁶(97-digit number)

54536323205533322498…15890441532788940799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.453 × 10⁹⁶(97-digit number)

54536323205533322498…15890441532788940801

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

1.090 × 10⁹⁷(98-digit number)

10907264641106664499…31780883065577881599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.090 × 10⁹⁷(98-digit number)

10907264641106664499…31780883065577881601

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 391114

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 fe4b62de80b325f7738fa0676e89b0c48261efb358819842cca43c2023cbe52f

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 #391,114 on Chainz ↗

Block #391,114

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