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Block #473,839

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/4/2014, 4:57:48 AM Β· Difficulty 10.4450 Β· 6,356,710 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
719cb412969a92fd6a6a8c54fbe60036ae42919b6c6a687bf0cc81b92fa0688b
View on Chainz β†—

Height

#473,839

Difficulty

10.445014

Transactions

1

Size

199 B

Version

2

Bits

0a71ec6c

Nonce

1,497,463,785

Timestamp

4/4/2014, 4:57:48 AM

Confirmations

6,356,710

Merkle Root

ad58e1dc61d95e2bbfdb1ecb032dc9a12a4325c0593d86554b8418ad2ba11b86
Transactions (1)
Coinbasead58e1dc61d95e…8418ad2ba11b86
1 in β†’ 1 out9.1500 XPM109 B
AS3Lfdp4…iuVV5HeS
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.

3.746 Γ— 10⁹⁴(95-digit number)
37467256668214017753…34076508003338306660
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
3.746 Γ— 10⁹⁴(95-digit number)
37467256668214017753…34076508003338306659
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.746 Γ— 10⁹⁴(95-digit number)
37467256668214017753…34076508003338306661
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
7.493 Γ— 10⁹⁴(95-digit number)
74934513336428035507…68153016006676613319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.493 Γ— 10⁹⁴(95-digit number)
74934513336428035507…68153016006676613321
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
1.498 Γ— 10⁹⁡(96-digit number)
14986902667285607101…36306032013353226639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.498 Γ— 10⁹⁡(96-digit number)
14986902667285607101…36306032013353226641
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
2.997 Γ— 10⁹⁡(96-digit number)
29973805334571214202…72612064026706453279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.997 Γ— 10⁹⁡(96-digit number)
29973805334571214202…72612064026706453281
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
5.994 Γ— 10⁹⁡(96-digit number)
59947610669142428405…45224128053412906559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.994 Γ— 10⁹⁡(96-digit number)
59947610669142428405…45224128053412906561
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

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 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
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 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 473839

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 719cb412969a92fd6a6a8c54fbe60036ae42919b6c6a687bf0cc81b92fa0688b

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 #473,839 on Chainz β†—
Circulating Supply:57,888,550 XPMΒ·at block #6,830,548 Β· updates every 60s
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