Home/Chain Registry/Block #854,158

Block #854,158

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 12/15/2014, 10:08:52 AM · Difficulty 10.9688 · 5,978,000 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a1f48a6d9f6180404e70cf9240b4dae2126ff34113aef000316ad7cddffaf4d4

View on Chainz ↗

Height

#854,158

Difficulty

10.968757

Transactions

Size

842 B

Version

Bits

0af80070

Nonce

689,355,950

Timestamp

12/15/2014, 10:08:52 AM

Confirmations

5,978,000

Merkle Root

48952abaf2d16bd4eaa5cefb799f354c3f2f8d2c5b3b7999563bcbd7faeef529

Transactions (4)

Coinbaseb43893680d64c1…341de0870e9050

1 in → 1 out8.3454 XPM109 B

AbdJb3m4…5GZ6gmD5

e52602eade4406…d4e169af06cf70

1 in → 2 out0.0655 XPM225 B

AVucpo95…A4FkseBN AQSKGLzs…eeK2humi

ef1bd12eb4ce16…c2dc16bc8160f0

1 in → 1 out0.0118 XPM192 B

ANHW5BQ2…s5qbKyHq

369dc4d0b63f7f…e2718f5b29a5bb

1 in → 2 out0.0263 XPM226 B

AHEwjGHA…4BP1wqGJ AVvGtQqZ…WbtRi1rX

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.

9.409 × 10⁹⁴(95-digit number)

94098001532510452864…71606322135109797120

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

9.409 × 10⁹⁴(95-digit number)

94098001532510452864…71606322135109797119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.409 × 10⁹⁴(95-digit number)

94098001532510452864…71606322135109797121

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

1.881 × 10⁹⁵(96-digit number)

18819600306502090572…43212644270219594239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.881 × 10⁹⁵(96-digit number)

18819600306502090572…43212644270219594241

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

3.763 × 10⁹⁵(96-digit number)

37639200613004181145…86425288540439188479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.763 × 10⁹⁵(96-digit number)

37639200613004181145…86425288540439188481

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

7.527 × 10⁹⁵(96-digit number)

75278401226008362291…72850577080878376959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.527 × 10⁹⁵(96-digit number)

75278401226008362291…72850577080878376961

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

1.505 × 10⁹⁶(97-digit number)

15055680245201672458…45701154161756753919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.505 × 10⁹⁶(97-digit number)

15055680245201672458…45701154161756753921

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

3.011 × 10⁹⁶(97-digit number)

30111360490403344916…91402308323513507839

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 854158

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 a1f48a6d9f6180404e70cf9240b4dae2126ff34113aef000316ad7cddffaf4d4

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 #854,158 on Chainz ↗

Block #854,158

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