Home/Chain Registry/Block #496,731

Block #496,731

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/17/2014, 5:52:40 AM · Difficulty 10.7583 · 6,299,184 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6fd0bdfbc98419e2272755bc343ab45630f68ecbb5ff55ca1873d5084685e5a3

View on Chainz ↗

Height

#496,731

Difficulty

10.758345

Transactions

Size

1.83 KB

Version

Bits

0ac222e3

Nonce

5,122

Timestamp

4/17/2014, 5:52:40 AM

Confirmations

6,299,184

Merkle Root

69be3b6ed73cbbad65105c805ea69201858e6b2eb04393f17a53f8019e5d8c07

Transactions (4)

Coinbase6b35afa38b643c…117fab05697fe5

1 in → 22 out8.6600 XPM811 B

AGz9gyZW…bo8NYQpw AMVf7Jrg…xd5AVR7C AXCpMYgL…1r94ZQDa AMW1p9oT…2TzdaZxH AJ6GifLQ…DERUewSz

b6e0d9adb7451e…701b2135bcb3d1

3 in → 2 out26.6300 XPM523 B

APUrqSLj…KxVrZKf8 ANGms7De…RQBjncXS

c8ccd55be477d5…445f15017c182d

1 in → 2 out8.7100 XPM225 B

AN3Q4Fzx…HFdoRz47 AJLtWo27…MucxF76p

dc2ce09e7e00ee…2f5ff044db4881

1 in → 2 out8.7100 XPM225 B

AJQVDkM3…9EVf3Vrd AcmEg7we…q96PifEQ

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.

1.069 × 10¹⁰³(104-digit number)

10698679714511213491…21644259192816098560

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

1.069 × 10¹⁰³(104-digit number)

10698679714511213491…21644259192816098559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.069 × 10¹⁰³(104-digit number)

10698679714511213491…21644259192816098561

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

2.139 × 10¹⁰³(104-digit number)

21397359429022426983…43288518385632197119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.139 × 10¹⁰³(104-digit number)

21397359429022426983…43288518385632197121

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

4.279 × 10¹⁰³(104-digit number)

42794718858044853966…86577036771264394239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.279 × 10¹⁰³(104-digit number)

42794718858044853966…86577036771264394241

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

8.558 × 10¹⁰³(104-digit number)

85589437716089707932…73154073542528788479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.558 × 10¹⁰³(104-digit number)

85589437716089707932…73154073542528788481

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

1.711 × 10¹⁰⁴(105-digit number)

17117887543217941586…46308147085057576959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.711 × 10¹⁰⁴(105-digit number)

17117887543217941586…46308147085057576961

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 496731

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 6fd0bdfbc98419e2272755bc343ab45630f68ecbb5ff55ca1873d5084685e5a3

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 #496,731 on Chainz ↗