Home/Chain Registry/Block #154,880

Block #154,880

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/7/2013, 11:26:54 PM · Difficulty 9.8647 · 6,637,046 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

12bb30724ed160015d6c0e8c0b37c22edf11f65680d8da36a43d5022014b1d9e

View on Chainz ↗

Height

#154,880

Difficulty

9.864711

Transactions

Size

201 B

Version

Bits

09dd5db2

Nonce

48,189

Timestamp

9/7/2013, 11:26:54 PM

Confirmations

6,637,046

Merkle Root

c9d3984e56619ef8da8fc00cdacf967424fdccac61005dde9e574fff65f9f4d6

Transactions (1)

Coinbasec9d3984e56619e…574fff65f9f4d6

1 in → 1 out10.2600 XPM109 B

AFuhUM91…DrTVQzbX

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.

4.495 × 10⁹⁸(99-digit number)

44951466748931576641…06992165806118479760

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

4.495 × 10⁹⁸(99-digit number)

44951466748931576641…06992165806118479759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.495 × 10⁹⁸(99-digit number)

44951466748931576641…06992165806118479761

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

8.990 × 10⁹⁸(99-digit number)

89902933497863153283…13984331612236959519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.990 × 10⁹⁸(99-digit number)

89902933497863153283…13984331612236959521

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

1.798 × 10⁹⁹(100-digit number)

17980586699572630656…27968663224473919039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.798 × 10⁹⁹(100-digit number)

17980586699572630656…27968663224473919041

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

3.596 × 10⁹⁹(100-digit number)

35961173399145261313…55937326448947838079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.596 × 10⁹⁹(100-digit number)

35961173399145261313…55937326448947838081

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

7.192 × 10⁹⁹(100-digit number)

71922346798290522626…11874652897895676159

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 154880

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 12bb30724ed160015d6c0e8c0b37c22edf11f65680d8da36a43d5022014b1d9e

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 #154,880 on Chainz ↗