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Block #496,442

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/17/2014, 2:34:12 AM Β· Difficulty 10.7539 Β· 6,304,571 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ca29dd98af0197525506d8b6372d5191910d1d2a251d6cd414f8d7e5f6f89b05
View on Chainz β†—

Height

#496,442

Difficulty

10.753866

Transactions

1

Size

207 B

Version

2

Bits

0ac0fd5f

Nonce

291,949,691

Timestamp

4/17/2014, 2:34:12 AM

Confirmations

6,304,571

Merkle Root

432dae4039764ee75f29125f261045a22418e79fdcc1aacd6f60bd4f186d7513
Transactions (1)
Coinbase432dae4039764e…60bd4f186d7513
1 in β†’ 1 out8.6300 XPM116 B
AbwWkWZt…kawDhufa
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.

1.396 Γ— 10⁹⁷(98-digit number)
13966872914163086844…52661633277591076200
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
1.396 Γ— 10⁹⁷(98-digit number)
13966872914163086844…52661633277591076199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.396 Γ— 10⁹⁷(98-digit number)
13966872914163086844…52661633277591076201
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
2.793 Γ— 10⁹⁷(98-digit number)
27933745828326173688…05323266555182152399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.793 Γ— 10⁹⁷(98-digit number)
27933745828326173688…05323266555182152401
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
5.586 Γ— 10⁹⁷(98-digit number)
55867491656652347376…10646533110364304799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.586 Γ— 10⁹⁷(98-digit number)
55867491656652347376…10646533110364304801
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
1.117 Γ— 10⁹⁸(99-digit number)
11173498331330469475…21293066220728609599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.117 Γ— 10⁹⁸(99-digit number)
11173498331330469475…21293066220728609601
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
2.234 Γ— 10⁹⁸(99-digit number)
22346996662660938950…42586132441457219199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.234 Γ— 10⁹⁸(99-digit number)
22346996662660938950…42586132441457219201
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 496442

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 ca29dd98af0197525506d8b6372d5191910d1d2a251d6cd414f8d7e5f6f89b05

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 #496,442 on Chainz β†—
Circulating Supply:57,652,165 XPMΒ·at block #6,801,012 Β· updates every 60s
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