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Block #1,239,610

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/16/2015, 5:24:30 PM · Difficulty 10.7576 · 5,556,695 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

67b42c279d1eb440aa655b5dfd3507bfa9a3a8ae5fc9f78045de00644eaed47c

View on Chainz ↗

Height

#1,239,610

Difficulty

10.757614

Transactions

Size

244 B

Version

Bits

0ac1f2ff

Nonce

11,899,533

Timestamp

9/16/2015, 5:24:30 PM

Confirmations

5,556,695

Merkle Root

ca0ae4be93ccdd426efbbe01d24ee462e92b2d9ba1789ef00a46fd972e3852a1

Transactions (1)

Coinbaseca0ae4be93ccdd…46fd972e3852a1

1 in → 2 out8.6300 XPM152 B

AVsg8K1F…ZPDrnoUR ALPu3s2c…EJXLjVFh

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.

1.107 × 10¹⁰⁰(101-digit number)

11078064108373369577…72429544808230748160

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

1.107 × 10¹⁰⁰(101-digit number)

11078064108373369577…72429544808230748159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.107 × 10¹⁰⁰(101-digit number)

11078064108373369577…72429544808230748161

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

2.215 × 10¹⁰⁰(101-digit number)

22156128216746739154…44859089616461496319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.215 × 10¹⁰⁰(101-digit number)

22156128216746739154…44859089616461496321

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

4.431 × 10¹⁰⁰(101-digit number)

44312256433493478308…89718179232922992639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.431 × 10¹⁰⁰(101-digit number)

44312256433493478308…89718179232922992641

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

8.862 × 10¹⁰⁰(101-digit number)

88624512866986956616…79436358465845985279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.862 × 10¹⁰⁰(101-digit number)

88624512866986956616…79436358465845985281

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

1.772 × 10¹⁰¹(102-digit number)

17724902573397391323…58872716931691970559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.772 × 10¹⁰¹(102-digit number)

17724902573397391323…58872716931691970561

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 1239610

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 67b42c279d1eb440aa655b5dfd3507bfa9a3a8ae5fc9f78045de00644eaed47c

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 #1,239,610 on Chainz ↗