Home/Chain Registry/Block #60,167

Block #60,167

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/18/2013, 6:31:10 AM · Difficulty 8.9681 · 6,767,000 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

65f63e5714e01844c692abf6998ecb047c16b3e585fa036b4a508fbe90074cdb

View on Chainz ↗

Height

#60,167

Difficulty

8.968059

Transactions

Size

198 B

Version

Bits

08f7d2bd

Nonce

234

Timestamp

7/18/2013, 6:31:10 AM

Confirmations

6,767,000

Merkle Root

9d6e6855e96522a7d35bcc908b1c58752198eafc56542fe96b46d1d2519b05c6

Transactions (1)

Coinbase9d6e6855e96522…46d1d2519b05c6

1 in → 1 out12.4200 XPM109 B

AVVGqzEE…ATovjxU2

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.

3.966 × 10⁹¹(92-digit number)

39669694220746185103…57931480041662033920

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

3.966 × 10⁹¹(92-digit number)

39669694220746185103…57931480041662033919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.966 × 10⁹¹(92-digit number)

39669694220746185103…57931480041662033921

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

7.933 × 10⁹¹(92-digit number)

79339388441492370207…15862960083324067839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.933 × 10⁹¹(92-digit number)

79339388441492370207…15862960083324067841

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

1.586 × 10⁹²(93-digit number)

15867877688298474041…31725920166648135679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.586 × 10⁹²(93-digit number)

15867877688298474041…31725920166648135681

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

3.173 × 10⁹²(93-digit number)

31735755376596948083…63451840333296271359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.173 × 10⁹²(93-digit number)

31735755376596948083…63451840333296271361

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

6.347 × 10⁹²(93-digit number)

63471510753193896166…26903680666592542719

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 60167

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 65f63e5714e01844c692abf6998ecb047c16b3e585fa036b4a508fbe90074cdb

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 #60,167 on Chainz ↗

Block #60,167

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