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Block #657,608

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/1/2014, 8:25:40 AM Β· Difficulty 10.9562 Β· 6,169,009 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
2560ef38980a8535e0cf1346d74399200d412fee19e4d7b39632f32567e5c9ca
View on Chainz β†—

Height

#657,608

Difficulty

10.956213

Transactions

1

Size

243 B

Version

2

Bits

0af4ca63

Nonce

331,876,435

Timestamp

8/1/2014, 8:25:40 AM

Confirmations

6,169,009

Merkle Root

6365a526e25680c0df05f0b0bf5ab3a61077d25a9c6b1036d5f70c46e868bad5
Transactions (1)
Coinbase6365a526e25680…f70c46e868bad5
1 in β†’ 2 out8.3200 XPM152 B
ASLBrKY8…73inofKNALPu3s2c…EJXLjVFh
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.362 Γ— 10⁹⁷(98-digit number)
13620424932002984673…55274828737651486720
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— 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 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
1.362 Γ— 10⁹⁷(98-digit number)
13620424932002984673…55274828737651486719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.362 Γ— 10⁹⁷(98-digit number)
13620424932002984673…55274828737651486721
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
2.724 Γ— 10⁹⁷(98-digit number)
27240849864005969347…10549657475302973439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.724 Γ— 10⁹⁷(98-digit number)
27240849864005969347…10549657475302973441
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
5.448 Γ— 10⁹⁷(98-digit number)
54481699728011938694…21099314950605946879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.448 Γ— 10⁹⁷(98-digit number)
54481699728011938694…21099314950605946881
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
1.089 Γ— 10⁹⁸(99-digit number)
10896339945602387738…42198629901211893759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.089 Γ— 10⁹⁸(99-digit number)
10896339945602387738…42198629901211893761
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
2.179 Γ— 10⁹⁸(99-digit number)
21792679891204775477…84397259802423787519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.179 Γ— 10⁹⁸(99-digit number)
21792679891204775477…84397259802423787521
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
4.358 Γ— 10⁹⁸(99-digit number)
43585359782409550955…68794519604847575039
Verify on FactorDB β†—Wolfram Alpha β†—

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 β€” the large number shown above β€” 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 β†’
β˜…β˜…β˜…β˜†β˜†
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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” 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 βˆ’ 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 657608

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 2560ef38980a8535e0cf1346d74399200d412fee19e4d7b39632f32567e5c9ca

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 β†’ Debug Window β†’ 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 #657,608 on Chainz β†—
Circulating Supply:57,857,089 XPMΒ·at block #6,826,616 Β· updates every 60s
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