Home/Chain Registry/Block #1,325,154

Block #1,325,154

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 11/13/2015, 10:02:16 AM · Difficulty 10.8539 · 5,501,101 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

28597cd0b153da2c05ee25cbafdfb4fdba4e7d3eb681bd41e18cca830508ead4

View on Chainz ↗

Height

#1,325,154

Difficulty

10.853854

Transactions

Size

1005 B

Version

Bits

0ada9628

Nonce

348,891,193

Timestamp

11/13/2015, 10:02:16 AM

Confirmations

5,501,101

Merkle Root

c8bf3e9846b5cd1ea247af83fe6a4e1319f8f59ac5b431a2b752b9600a8510c1

Transactions (2)

Coinbasea11b21c2da8392…9c80932037e826

1 in → 1 out8.4900 XPM110 B

ALT8kmWc…MZoUWD6J

74d3781614920f…74bdaa5ef23659

1 in → 19 out7.8356 XPM804 B

AZdido3s…umKEg2dZ AG97kpGV…BGGHr9WA AXkdTXsM…cy69zhzv ARo9Rjx3…ybm7RKTT ARskDAYq…wf1LaozE

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.

6.665 × 10⁹⁷(98-digit number)

66655234238894495555…16914033668036689920

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

6.665 × 10⁹⁷(98-digit number)

66655234238894495555…16914033668036689919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.665 × 10⁹⁷(98-digit number)

66655234238894495555…16914033668036689921

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

1.333 × 10⁹⁸(99-digit number)

13331046847778899111…33828067336073379839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.333 × 10⁹⁸(99-digit number)

13331046847778899111…33828067336073379841

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

2.666 × 10⁹⁸(99-digit number)

26662093695557798222…67656134672146759679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.666 × 10⁹⁸(99-digit number)

26662093695557798222…67656134672146759681

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

5.332 × 10⁹⁸(99-digit number)

53324187391115596444…35312269344293519359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.332 × 10⁹⁸(99-digit number)

53324187391115596444…35312269344293519361

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

1.066 × 10⁹⁹(100-digit number)

10664837478223119288…70624538688587038719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.066 × 10⁹⁹(100-digit number)

10664837478223119288…70624538688587038721

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

2.132 × 10⁹⁹(100-digit number)

21329674956446238577…41249077377174077439

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 1325154

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 28597cd0b153da2c05ee25cbafdfb4fdba4e7d3eb681bd41e18cca830508ead4

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 #1,325,154 on Chainz ↗

Block #1,325,154

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