Home/Chain Registry/Block #654,106

Block #654,106

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 7/29/2014, 11:45:46 PM · Difficulty 10.9552 · 6,140,822 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

abd7885a5575cb76bc3bdc66aae885f8e6e37e1f70965a845322b72ce618dcda

View on Chainz ↗

Height

#654,106

Difficulty

10.955207

Transactions

Size

72.58 KB

Version

Bits

0af4887a

Nonce

2,016,060,420

Timestamp

7/29/2014, 11:45:46 PM

Confirmations

6,140,822

Merkle Root

d8a2b8152f2d4a7b4a58e53642e61d734e363631d13cf3bced1fe042321b8345

Transactions (2)

Coinbasedaa79f278d5d00…da1118a79ad8d2

1 in → 1 out9.0700 XPM116 B

ANSXnLY2…Sd25TjkD

8cea2727bc1458…90001d4011b8d5

500 in → 2 out500.0100 XPM72.37 KB

AJYhXqvD…fCNBH85f AUE5QneS…bDZqwQ1J

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.

3.685 × 10⁹⁵(96-digit number)

36858242604828003341…67938529717550983040

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

3.685 × 10⁹⁵(96-digit number)

36858242604828003341…67938529717550983039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.685 × 10⁹⁵(96-digit number)

36858242604828003341…67938529717550983041

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

7.371 × 10⁹⁵(96-digit number)

73716485209656006683…35877059435101966079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.371 × 10⁹⁵(96-digit number)

73716485209656006683…35877059435101966081

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

1.474 × 10⁹⁶(97-digit number)

14743297041931201336…71754118870203932159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.474 × 10⁹⁶(97-digit number)

14743297041931201336…71754118870203932161

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

2.948 × 10⁹⁶(97-digit number)

29486594083862402673…43508237740407864319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.948 × 10⁹⁶(97-digit number)

29486594083862402673…43508237740407864321

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

5.897 × 10⁹⁶(97-digit number)

58973188167724805346…87016475480815728639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.897 × 10⁹⁶(97-digit number)

58973188167724805346…87016475480815728641

Verify on FactorDB ↗Wolfram Alpha ↗

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

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.179 × 10⁹⁷(98-digit number)

11794637633544961069…74032950961631457279

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

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 654106

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 abd7885a5575cb76bc3bdc66aae885f8e6e37e1f70965a845322b72ce618dcda

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 #654,106 on Chainz ↗