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Block #37,315

TWNLength 7★☆☆☆☆

Bi-Twin Chain · Discovered 7/14/2013, 10:30:49 AM · Difficulty 7.9961 · 6,770,520 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

588122c0fc297a5208791a1df18e20d7082ad8622c3e1f58033c2b0e8398426c

View on Chainz ↗

Height

#37,315

Difficulty

7.996087

Transactions

Size

199 B

Version

Bits

07feff93

Nonce

322

Timestamp

7/14/2013, 10:30:49 AM

Confirmations

6,770,520

Merkle Root

8ea670cc4acaeb911d29ee0b6829a03f2a2d509ec4b1d217624353230bc7623f

Transactions (1)

Coinbase8ea670cc4acaeb…4353230bc7623f

1 in → 1 out15.6200 XPM110 B

AVPSPN5q…TLjkTDWF

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.

4.944 × 10⁹¹(92-digit number)

49445536759449212965…07903998950413780960

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

4.944 × 10⁹¹(92-digit number)

49445536759449212965…07903998950413780959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.944 × 10⁹¹(92-digit number)

49445536759449212965…07903998950413780961

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

9.889 × 10⁹¹(92-digit number)

98891073518898425931…15807997900827561919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.889 × 10⁹¹(92-digit number)

98891073518898425931…15807997900827561921

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

1.977 × 10⁹²(93-digit number)

19778214703779685186…31615995801655123839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.977 × 10⁹²(93-digit number)

19778214703779685186…31615995801655123841

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

3.955 × 10⁹²(93-digit number)

39556429407559370372…63231991603310247679

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 7 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 7

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 37315

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 588122c0fc297a5208791a1df18e20d7082ad8622c3e1f58033c2b0e8398426c

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 #37,315 on Chainz ↗

Block #37,315

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