Home/Chain Registry/Block #1,252,879

Block #1,252,879

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/25/2015, 12:05:06 PM · Difficulty 10.7864 · 5,539,888 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

abcd7b70251d13ea09c41c18bb7bc900aeb7b8f47add67828ce081287f03582d

View on Chainz ↗

Height

#1,252,879

Difficulty

10.786406

Transactions

Size

199 B

Version

Bits

0ac951e4

Nonce

1,933,816,726

Timestamp

9/25/2015, 12:05:06 PM

Confirmations

5,539,888

Merkle Root

5b1d2a92379f6eaa4da51dcdbe9f623eea1ffe5338c13bb620bdbf3a34ad3814

Transactions (1)

Coinbase5b1d2a92379f6e…bdbf3a34ad3814

1 in → 1 out8.5800 XPM110 B

AK46ezvf…HJJJxBHp

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.

5.342 × 10⁹²(93-digit number)

53423825462393544498…69238286111067784640

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

5.342 × 10⁹²(93-digit number)

53423825462393544498…69238286111067784639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.342 × 10⁹²(93-digit number)

53423825462393544498…69238286111067784641

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

1.068 × 10⁹³(94-digit number)

10684765092478708899…38476572222135569279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.068 × 10⁹³(94-digit number)

10684765092478708899…38476572222135569281

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

2.136 × 10⁹³(94-digit number)

21369530184957417799…76953144444271138559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.136 × 10⁹³(94-digit number)

21369530184957417799…76953144444271138561

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

4.273 × 10⁹³(94-digit number)

42739060369914835598…53906288888542277119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.273 × 10⁹³(94-digit number)

42739060369914835598…53906288888542277121

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

8.547 × 10⁹³(94-digit number)

85478120739829671197…07812577777084554239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.547 × 10⁹³(94-digit number)

85478120739829671197…07812577777084554241

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 1252879

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 abcd7b70251d13ea09c41c18bb7bc900aeb7b8f47add67828ce081287f03582d

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 #1,252,879 on Chainz ↗