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Block #497,051

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/17/2014, 9:48:47 AM Β· Difficulty 10.7623 Β· 6,329,315 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
dec34248f9df361f8e69288695c1a9588098bebc73b6bc777399577d8e7155ef
View on Chainz β†—

Height

#497,051

Difficulty

10.762301

Transactions

2

Size

427 B

Version

2

Bits

0ac32629

Nonce

34,791

Timestamp

4/17/2014, 9:48:47 AM

Confirmations

6,329,315

Merkle Root

adada30c0c9622533a1495b0791099a0a01bae4a194613c1d7183011754eb96c
Transactions (2)
Coinbasecce3414f78e883…7873c778688a3c
1 in β†’ 1 out8.6300 XPM110 B
AJTzKnqz…VZaUG2F4
1250f04e4f2209…082e52b39b0a47
1 in β†’ 2 out5.1572 XPM226 B
AWm9M3e7…snyj6iRbAGpsG4ez…9CixeeJN
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.

2.689 Γ— 10⁹⁷(98-digit number)
26898286501866901602…13361628364122828800
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
2.689 Γ— 10⁹⁷(98-digit number)
26898286501866901602…13361628364122828799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.689 Γ— 10⁹⁷(98-digit number)
26898286501866901602…13361628364122828801
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
5.379 Γ— 10⁹⁷(98-digit number)
53796573003733803204…26723256728245657599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.379 Γ— 10⁹⁷(98-digit number)
53796573003733803204…26723256728245657601
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
1.075 Γ— 10⁹⁸(99-digit number)
10759314600746760640…53446513456491315199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.075 Γ— 10⁹⁸(99-digit number)
10759314600746760640…53446513456491315201
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
2.151 Γ— 10⁹⁸(99-digit number)
21518629201493521281…06893026912982630399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.151 Γ— 10⁹⁸(99-digit number)
21518629201493521281…06893026912982630401
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
4.303 Γ— 10⁹⁸(99-digit number)
43037258402987042563…13786053825965260799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.303 Γ— 10⁹⁸(99-digit number)
43037258402987042563…13786053825965260801
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 497051

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 dec34248f9df361f8e69288695c1a9588098bebc73b6bc777399577d8e7155ef

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 #497,051 on Chainz β†—
Circulating Supply:57,855,072 XPMΒ·at block #6,826,365 Β· updates every 60s
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