Home/Chain Registry/Block #3,505,336

Block #3,505,336

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 1/8/2020, 1:23:55 PM · Difficulty 10.9306 · 3,328,081 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
00bb0c4a70532146f73f1abc88aef808f4d91fc139bef580426f0b0dded40497

Difficulty

10.930596

Transactions

12

Size

73.81 KB

Version

2

Bits

0aee3b84

Nonce

229,886,798

Timestamp

1/8/2020, 1:23:55 PM

Confirmations

3,328,081

Merkle Root

86c63eeef28bad02c928325379e83be40b00b36068bdc25a0bc2a800c9a2b27f
Transactions (12)
1 in → 1 out9.1700 XPM109 B
50 in → 1 out199.9200 XPM7.26 KB
50 in → 1 out199.9200 XPM7.26 KB
50 in → 1 out199.9200 XPM7.26 KB
50 in → 1 out199.9200 XPM7.27 KB
50 in → 1 out3922.4000 XPM7.26 KB
50 in → 1 out199.9200 XPM7.27 KB
50 in → 1 out199.9200 XPM7.27 KB
50 in → 1 out199.9200 XPM7.27 KB
50 in → 1 out199.9200 XPM7.27 KB
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.

7.716 × 10⁹⁷(98-digit number)
77162826513876373077…90898313885637345280
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
7.716 × 10⁹⁷(98-digit number)
77162826513876373077…90898313885637345279
Verify on FactorDB ↗Wolfram Alpha ↗
origin + 1
7.716 × 10⁹⁷(98-digit number)
77162826513876373077…90898313885637345281
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
1.543 × 10⁹⁸(99-digit number)
15432565302775274615…81796627771274690559
Verify on FactorDB ↗Wolfram Alpha ↗
2^1 × origin + 1
1.543 × 10⁹⁸(99-digit number)
15432565302775274615…81796627771274690561
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
3.086 × 10⁹⁸(99-digit number)
30865130605550549231…63593255542549381119
Verify on FactorDB ↗Wolfram Alpha ↗
2^2 × origin + 1
3.086 × 10⁹⁸(99-digit number)
30865130605550549231…63593255542549381121
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
6.173 × 10⁹⁸(99-digit number)
61730261211101098462…27186511085098762239
Verify on FactorDB ↗Wolfram Alpha ↗
2^3 × origin + 1
6.173 × 10⁹⁸(99-digit number)
61730261211101098462…27186511085098762241
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
1.234 × 10⁹⁹(100-digit number)
12346052242220219692…54373022170197524479
Verify on FactorDB ↗Wolfram Alpha ↗
2^4 × origin + 1
1.234 × 10⁹⁹(100-digit number)
12346052242220219692…54373022170197524481
Verify on FactorDB ↗Wolfram Alpha ↗
Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)
Level 5 — Twin Prime Pair (2^5 × origin ± 1)
2^5 × origin − 1
2.469 × 10⁹⁹(100-digit number)
24692104484440439384…08746044340395048959
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 3505336

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 00bb0c4a70532146f73f1abc88aef808f4d91fc139bef580426f0b0dded40497

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 #3,505,336 on Chainz ↗
Circulating Supply:57,911,538 XPM·at block #6,833,416 · updates every 60s
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