Home/Chain Registry/Block #137,373

Block #137,373

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/27/2013, 6:48:40 PM · Difficulty 9.8209 · 6,654,623 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

025da9b12e4717dc7a67a80a80e6b41dc543afcc71b2d260ebe7e4b48feda47f

View on Chainz ↗

Height

#137,373

Difficulty

9.820887

Transactions

Size

204 B

Version

Bits

09d225a1

Nonce

16,779,788

Timestamp

8/27/2013, 6:48:40 PM

Confirmations

6,654,623

Merkle Root

f125d68652ba3d2ebe2dd7dfaf6ebc2a002c47f3af4c64199e3cadf7455918aa

Transactions (1)

Coinbasef125d68652ba3d…3cadf7455918aa

1 in → 1 out10.3500 XPM112 B

AT5A2KL6…CT16n6i2

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.

1.758 × 10¹⁰⁰(101-digit number)

17587035687864675621…75294125673815457600

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

1.758 × 10¹⁰⁰(101-digit number)

17587035687864675621…75294125673815457599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.758 × 10¹⁰⁰(101-digit number)

17587035687864675621…75294125673815457601

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

3.517 × 10¹⁰⁰(101-digit number)

35174071375729351243…50588251347630915199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.517 × 10¹⁰⁰(101-digit number)

35174071375729351243…50588251347630915201

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

7.034 × 10¹⁰⁰(101-digit number)

70348142751458702486…01176502695261830399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.034 × 10¹⁰⁰(101-digit number)

70348142751458702486…01176502695261830401

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

1.406 × 10¹⁰¹(102-digit number)

14069628550291740497…02353005390523660799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.406 × 10¹⁰¹(102-digit number)

14069628550291740497…02353005390523660801

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

2.813 × 10¹⁰¹(102-digit number)

28139257100583480994…04706010781047321599

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 137373

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 025da9b12e4717dc7a67a80a80e6b41dc543afcc71b2d260ebe7e4b48feda47f

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 #137,373 on Chainz ↗