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Block #1,207,479

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/25/2015, 3:44:15 AM · Difficulty 10.7737 · 5,631,621 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3c0489b1bc0747ebc0952b368b70dd9e56dff6aa0444457245540e6dfc68410a

View on Chainz ↗

Height

#1,207,479

Difficulty

10.773739

Transactions

Size

15.02 KB

Version

Bits

0ac613c1

Nonce

1,041,724,065

Timestamp

8/25/2015, 3:44:15 AM

Confirmations

5,631,621

Merkle Root

7baacd5906236a8de8d7d1c73d47c51e20855d52a0a0ee5422e27f6aae7c0811

Transactions (2)

Coinbase7672dfd9f5281f…4972330b5361ee

1 in → 1 out8.7800 XPM110 B

AaxVNVPy…W5g5cr8u

9dad9a8a29ed73…846a4bec6256ac

102 in → 2 out574.0100 XPM14.82 KB

AYHqVxeQ…xdtpawf5 AMxkbHZT…kPGYvuj2

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.

5.272 × 10⁹³(94-digit number)

52720132407738991249…13652537679907622880

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

5.272 × 10⁹³(94-digit number)

52720132407738991249…13652537679907622879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.272 × 10⁹³(94-digit number)

52720132407738991249…13652537679907622881

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

1.054 × 10⁹⁴(95-digit number)

10544026481547798249…27305075359815245759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.054 × 10⁹⁴(95-digit number)

10544026481547798249…27305075359815245761

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

2.108 × 10⁹⁴(95-digit number)

21088052963095596499…54610150719630491519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.108 × 10⁹⁴(95-digit number)

21088052963095596499…54610150719630491521

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

4.217 × 10⁹⁴(95-digit number)

42176105926191192999…09220301439260983039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.217 × 10⁹⁴(95-digit number)

42176105926191192999…09220301439260983041

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

8.435 × 10⁹⁴(95-digit number)

84352211852382385998…18440602878521966079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.435 × 10⁹⁴(95-digit number)

84352211852382385998…18440602878521966081

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

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 1207479

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 3c0489b1bc0747ebc0952b368b70dd9e56dff6aa0444457245540e6dfc68410a

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 #1,207,479 on Chainz ↗

Block #1,207,479

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