Home/Chain Registry/Block #60,540

Block #60,540

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/18/2013, 8:30:19 AM · Difficulty 8.9696 · 6,731,037 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

beb1fecb6c3a430a38b37b9e4c6f23cddf22f9b45b4f497b1ab67acb0b846613

View on Chainz ↗

Height

#60,540

Difficulty

8.969638

Transactions

Size

202 B

Version

Bits

08f83a37

Nonce

Timestamp

7/18/2013, 8:30:19 AM

Confirmations

6,731,037

Merkle Root

dacf51096a9913ef11ad7b6820b3b8f27d2bbbb7ba02bfc8659a5f6434dea9c4

Transactions (1)

Coinbasedacf51096a9913…9a5f6434dea9c4

1 in → 1 out12.4100 XPM109 B

AGBNLcL4…3pKe9W4g

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.

4.448 × 10¹⁰²(103-digit number)

44484366435620105937…69989683526708834750

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

4.448 × 10¹⁰²(103-digit number)

44484366435620105937…69989683526708834749

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.448 × 10¹⁰²(103-digit number)

44484366435620105937…69989683526708834751

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

8.896 × 10¹⁰²(103-digit number)

88968732871240211874…39979367053417669499

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.896 × 10¹⁰²(103-digit number)

88968732871240211874…39979367053417669501

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

1.779 × 10¹⁰³(104-digit number)

17793746574248042374…79958734106835338999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.779 × 10¹⁰³(104-digit number)

17793746574248042374…79958734106835339001

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

3.558 × 10¹⁰³(104-digit number)

35587493148496084749…59917468213670677999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.558 × 10¹⁰³(104-digit number)

35587493148496084749…59917468213670678001

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

7.117 × 10¹⁰³(104-digit number)

71174986296992169499…19834936427341355999

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 60540

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 beb1fecb6c3a430a38b37b9e4c6f23cddf22f9b45b4f497b1ab67acb0b846613

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 #60,540 on Chainz ↗