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Block #37,613

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/14/2013, 10:53:27 AM · Difficulty 8.0516 · 6,752,331 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2c822e5748393f2ba1ebbd589e27a3b31c855b70cd9373dc348b3457f0ab99a1

View on Chainz ↗

Height

#37,613

Difficulty

8.051609

Transactions

Size

201 B

Version

Bits

080d3637

Nonce

533

Timestamp

7/14/2013, 10:53:27 AM

Confirmations

6,752,331

Merkle Root

d61984c6548812dbd136a4600637095fffe0ef16038256407410f54f8eb520bf

Transactions (1)

Coinbased61984c6548812…10f54f8eb520bf

1 in → 1 out15.4000 XPM110 B

AMxKwCCc…EZ6JsCVT

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.

2.688 × 10⁹⁶(97-digit number)

26881773827925667369…41949567765008069280

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

2.688 × 10⁹⁶(97-digit number)

26881773827925667369…41949567765008069279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.688 × 10⁹⁶(97-digit number)

26881773827925667369…41949567765008069281

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

5.376 × 10⁹⁶(97-digit number)

53763547655851334739…83899135530016138559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.376 × 10⁹⁶(97-digit number)

53763547655851334739…83899135530016138561

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

1.075 × 10⁹⁷(98-digit number)

10752709531170266947…67798271060032277119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.075 × 10⁹⁷(98-digit number)

10752709531170266947…67798271060032277121

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

2.150 × 10⁹⁷(98-digit number)

21505419062340533895…35596542120064554239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.150 × 10⁹⁷(98-digit number)

21505419062340533895…35596542120064554241

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 8 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 8

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 37613

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 2c822e5748393f2ba1ebbd589e27a3b31c855b70cd9373dc348b3457f0ab99a1

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 #37,613 on Chainz ↗