Home/Chain Registry/Block #154,881

Block #154,881

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/7/2013, 11:28:01 PM · Difficulty 9.8647 · 6,639,462 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

03a0960afce8afe603a0b248e876e5d4f76e318a8e9eee2bd64f8518ef6676af

View on Chainz ↗

Height

#154,881

Difficulty

9.864699

Transactions

Size

200 B

Version

Bits

09dd5cef

Nonce

410,609

Timestamp

9/7/2013, 11:28:01 PM

Confirmations

6,639,462

Merkle Root

92cf17477646610c71e6ca3993503f6962657cc28f5786ef65ca17ea23c0c03d

Transactions (1)

Coinbase92cf1747764661…ca17ea23c0c03d

1 in → 1 out10.2600 XPM109 B

AGHegA75…QFCmbWoV

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.

6.536 × 10⁹⁶(97-digit number)

65366413287181897803…48506259452780155520

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

6.536 × 10⁹⁶(97-digit number)

65366413287181897803…48506259452780155519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.536 × 10⁹⁶(97-digit number)

65366413287181897803…48506259452780155521

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

1.307 × 10⁹⁷(98-digit number)

13073282657436379560…97012518905560311039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.307 × 10⁹⁷(98-digit number)

13073282657436379560…97012518905560311041

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

2.614 × 10⁹⁷(98-digit number)

26146565314872759121…94025037811120622079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.614 × 10⁹⁷(98-digit number)

26146565314872759121…94025037811120622081

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

5.229 × 10⁹⁷(98-digit number)

52293130629745518242…88050075622241244159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.229 × 10⁹⁷(98-digit number)

52293130629745518242…88050075622241244161

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

1.045 × 10⁹⁸(99-digit number)

10458626125949103648…76100151244482488319

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

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 154881

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 03a0960afce8afe603a0b248e876e5d4f76e318a8e9eee2bd64f8518ef6676af

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 #154,881 on Chainz ↗