Home/Chain Registry/Block #353,063

Block #353,063

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/10/2014, 5:28:01 PM · Difficulty 10.3187 · 6,492,641 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1ff4ec4e23b2a9685eab8d6ad4c88c67900e15c875c0492c752e23270cd92bb6

View on Chainz ↗

Height

#353,063

Difficulty

10.318732

Transactions

Size

2.94 KB

Version

Bits

0a51986d

Nonce

203,370

Timestamp

1/10/2014, 5:28:01 PM

Confirmations

6,492,641

Merkle Root

71bcd4159595f0653d24cfd763986c1178abfaa1e404dab13be6b4c028ea6f77

Transactions (4)

Coinbasee1ac263ebbbe7d…64d1f0efa05859

1 in → 27 out9.3800 XPM981 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AQwRN8bE…V8PsTcY9 AZemWJAo…6jhDtieG AZV4TwxQ…8JnQqSoH

6aa961defa70ce…393f57c1c689ce

7 in → 20 out66.4303 XPM1.45 KB

AHJFoooV…sAYN5LL4 AJE7armk…BPD71XGi APAQCo94…aBo4x9NP ANX1YLsv…GReXDPhr AUF1So9U…9k1XHL4c

cc364fc5be60c3…984e024941ba93

1 in → 2 out8.4191 XPM227 B

AbUnrgvg…1wBMZ3Eu ATqD8PcG…SfgdXWPf

0ae674c4350f2a…bdd1ecf67bf847

1 in → 2 out7.4055 XPM227 B

ARd47WCo…vXzjgLiX AMgHyyMh…8rAJSqoz

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.

5.964 × 10⁹⁶(97-digit number)

59644291491301017585…03197817210279495120

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

5.964 × 10⁹⁶(97-digit number)

59644291491301017585…03197817210279495119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.964 × 10⁹⁶(97-digit number)

59644291491301017585…03197817210279495121

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

1.192 × 10⁹⁷(98-digit number)

11928858298260203517…06395634420558990239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.192 × 10⁹⁷(98-digit number)

11928858298260203517…06395634420558990241

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

2.385 × 10⁹⁷(98-digit number)

23857716596520407034…12791268841117980479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.385 × 10⁹⁷(98-digit number)

23857716596520407034…12791268841117980481

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

4.771 × 10⁹⁷(98-digit number)

47715433193040814068…25582537682235960959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.771 × 10⁹⁷(98-digit number)

47715433193040814068…25582537682235960961

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

9.543 × 10⁹⁷(98-digit number)

95430866386081628136…51165075364471921919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.543 × 10⁹⁷(98-digit number)

95430866386081628136…51165075364471921921

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 353063

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 1ff4ec4e23b2a9685eab8d6ad4c88c67900e15c875c0492c752e23270cd92bb6

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 #353,063 on Chainz ↗

Block #353,063

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