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Block #648,514

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 7/26/2014, 8:51:55 AM Β· Difficulty 10.9515 Β· 6,176,236 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
86121023e03046e604a6ceea641100a803dae2f520faf869d90dba959cdec5d0
View on Chainz β†—

Height

#648,514

Difficulty

10.951538

Transactions

2

Size

432 B

Version

2

Bits

0af39803

Nonce

1,829,037,424

Timestamp

7/26/2014, 8:51:55 AM

Confirmations

6,176,236

Merkle Root

4ddc9cfa1d40846eaeb741302238cdb7df52b664d4ab77ccb094a1bed46331cc
Transactions (2)
Coinbase4466e4cf383a4d…4601bad743e0f8
1 in β†’ 1 out8.3300 XPM116 B
ANSXnLY2…Sd25TjkD
98784d5974e1ea…02861f035f08e0
1 in β†’ 2 out2.2327 XPM226 B
AGXqJki6…YNiMZGMNAZbFfg9x…5JqgRCNN
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.

3.045 Γ— 10⁹⁡(96-digit number)
30457887509242594895…64253800872916573200
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
3.045 Γ— 10⁹⁡(96-digit number)
30457887509242594895…64253800872916573199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.045 Γ— 10⁹⁡(96-digit number)
30457887509242594895…64253800872916573201
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
6.091 Γ— 10⁹⁡(96-digit number)
60915775018485189790…28507601745833146399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.091 Γ— 10⁹⁡(96-digit number)
60915775018485189790…28507601745833146401
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
1.218 Γ— 10⁹⁢(97-digit number)
12183155003697037958…57015203491666292799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.218 Γ— 10⁹⁢(97-digit number)
12183155003697037958…57015203491666292801
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
2.436 Γ— 10⁹⁢(97-digit number)
24366310007394075916…14030406983332585599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.436 Γ— 10⁹⁢(97-digit number)
24366310007394075916…14030406983332585601
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
4.873 Γ— 10⁹⁢(97-digit number)
48732620014788151832…28060813966665171199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.873 Γ— 10⁹⁢(97-digit number)
48732620014788151832…28060813966665171201
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
9.746 Γ— 10⁹⁢(97-digit number)
97465240029576303665…56121627933330342399
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 648514

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 86121023e03046e604a6ceea641100a803dae2f520faf869d90dba959cdec5d0

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 #648,514 on Chainz β†—
Circulating Supply:57,842,071 XPMΒ·at block #6,824,749 Β· updates every 60s
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