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Block #495,417

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/16/2014, 3:06:37 PM Β· Difficulty 10.7368 Β· 6,303,625 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d09af2c5aaa88a4c9d307c6650d29b5c1e16539a09be3bd3b323519df1b80047
View on Chainz β†—

Height

#495,417

Difficulty

10.736768

Transactions

2

Size

3.27 KB

Version

2

Bits

0abc9cd9

Nonce

26,669

Timestamp

4/16/2014, 3:06:37 PM

Confirmations

6,303,625

Merkle Root

4d8167c1669acf566eb3ffe7c3240b2d7913efb013995957303d39869d892155
Transactions (2)
Coinbaseb6e0c3a8652271…17596defc2c4c8
1 in β†’ 22 out8.6900 XPM811 B
AGz9gyZW…bo8NYQpwASgUri65…C7NLcyBgAMVf7Jrg…xd5AVR7CAXCpMYgL…1r94ZQDaAbPcCMg4…719q6mAX
f1be775057f79e…dd5463bd9fb908
16 in β†’ 2 out142.5573 XPM2.39 KB
AR5yT6bB…CakY9nXAAJ3Ex8Eq…CU3PNKgn
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.

2.470 Γ— 10⁹⁴(95-digit number)
24709590188628030335…63189772733373691520
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
2.470 Γ— 10⁹⁴(95-digit number)
24709590188628030335…63189772733373691519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.470 Γ— 10⁹⁴(95-digit number)
24709590188628030335…63189772733373691521
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
4.941 Γ— 10⁹⁴(95-digit number)
49419180377256060671…26379545466747383039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.941 Γ— 10⁹⁴(95-digit number)
49419180377256060671…26379545466747383041
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
9.883 Γ— 10⁹⁴(95-digit number)
98838360754512121342…52759090933494766079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.883 Γ— 10⁹⁴(95-digit number)
98838360754512121342…52759090933494766081
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
1.976 Γ— 10⁹⁡(96-digit number)
19767672150902424268…05518181866989532159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.976 Γ— 10⁹⁡(96-digit number)
19767672150902424268…05518181866989532161
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
3.953 Γ— 10⁹⁡(96-digit number)
39535344301804848536…11036363733979064319
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.953 Γ— 10⁹⁡(96-digit number)
39535344301804848536…11036363733979064321
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 495417

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 d09af2c5aaa88a4c9d307c6650d29b5c1e16539a09be3bd3b323519df1b80047

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 #495,417 on Chainz β†—
Circulating Supply:57,636,376 XPMΒ·at block #6,799,041 Β· updates every 60s
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