Home/Chain Registry/Block #1,305,074

Block #1,305,074

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 10/30/2015, 12:16:08 PM · Difficulty 10.8516 · 5,534,047 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

72813fdf30ec3b2677fca79be104fde161d2376e0ecaafa84d50f6e5122aeee9

View on Chainz ↗

Height

#1,305,074

Difficulty

10.851595

Transactions

Size

4.33 KB

Version

Bits

0ada021f

Nonce

816,233,622

Timestamp

10/30/2015, 12:16:08 PM

Confirmations

5,534,047

Merkle Root

672ec5d35bacf282dd2b495cd101937de3f4892d1e6f09e81442782fc5444b89

Transactions (2)

Coinbase93f2b24d9d84f2…93e5b51739c3a2

1 in → 1 out8.5300 XPM110 B

AUEugJmT…fofjEcFZ

7f39f0afc33bc7…89a25c6e536dcf

28 in → 2 out581.3141 XPM4.13 KB

AYK63jne…o3YRRAvu AZ7xo3ni…aXTAFhZR

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.

1.860 × 10⁹⁶(97-digit number)

18600516252996516534…68936772424372551680

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

1.860 × 10⁹⁶(97-digit number)

18600516252996516534…68936772424372551679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.860 × 10⁹⁶(97-digit number)

18600516252996516534…68936772424372551681

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

3.720 × 10⁹⁶(97-digit number)

37201032505993033069…37873544848745103359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.720 × 10⁹⁶(97-digit number)

37201032505993033069…37873544848745103361

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

7.440 × 10⁹⁶(97-digit number)

74402065011986066138…75747089697490206719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.440 × 10⁹⁶(97-digit number)

74402065011986066138…75747089697490206721

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

1.488 × 10⁹⁷(98-digit number)

14880413002397213227…51494179394980413439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.488 × 10⁹⁷(98-digit number)

14880413002397213227…51494179394980413441

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

2.976 × 10⁹⁷(98-digit number)

29760826004794426455…02988358789960826879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.976 × 10⁹⁷(98-digit number)

29760826004794426455…02988358789960826881

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

5.952 × 10⁹⁷(98-digit number)

59521652009588852910…05976717579921653759

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 1305074

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 72813fdf30ec3b2677fca79be104fde161d2376e0ecaafa84d50f6e5122aeee9

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 #1,305,074 on Chainz ↗

Block #1,305,074

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