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Block #574,669

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/3/2014, 11:34:00 AM Β· Difficulty 10.9678 Β· 6,225,522 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a54c7f93e1322ccfed0e8adf9a71aca2515d3d0edd6f6df418b61c3eefca63a7
View on Chainz β†—

Height

#574,669

Difficulty

10.967797

Transactions

2

Size

433 B

Version

2

Bits

0af7c191

Nonce

121,316,261

Timestamp

6/3/2014, 11:34:00 AM

Confirmations

6,225,522

Merkle Root

af69e39410fab7bf6d36eb2fd9eb2a9359059c3e923cdb58b8c457f93a87e96f
Transactions (2)
Coinbase564f79275d3e18…3f9b770ee51b56
1 in β†’ 1 out8.3100 XPM116 B
ANSXnLY2…Sd25TjkD
304e8cf29eca2e…e672ee1e47ee33
1 in β†’ 2 out6.5433 XPM226 B
AGdWVjRk…LFVsqCnKAbKnqU7B…NePSWk36
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.

3.864 Γ— 10⁹⁷(98-digit number)
38649231527325486444…59269055104047933200
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
3.864 Γ— 10⁹⁷(98-digit number)
38649231527325486444…59269055104047933199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.864 Γ— 10⁹⁷(98-digit number)
38649231527325486444…59269055104047933201
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
7.729 Γ— 10⁹⁷(98-digit number)
77298463054650972888…18538110208095866399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.729 Γ— 10⁹⁷(98-digit number)
77298463054650972888…18538110208095866401
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
1.545 Γ— 10⁹⁸(99-digit number)
15459692610930194577…37076220416191732799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.545 Γ— 10⁹⁸(99-digit number)
15459692610930194577…37076220416191732801
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
3.091 Γ— 10⁹⁸(99-digit number)
30919385221860389155…74152440832383465599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.091 Γ— 10⁹⁸(99-digit number)
30919385221860389155…74152440832383465601
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
6.183 Γ— 10⁹⁸(99-digit number)
61838770443720778310…48304881664766931199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.183 Γ— 10⁹⁸(99-digit number)
61838770443720778310…48304881664766931201
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 574669

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 a54c7f93e1322ccfed0e8adf9a71aca2515d3d0edd6f6df418b61c3eefca63a7

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 #574,669 on Chainz β†—
Circulating Supply:57,645,598 XPMΒ·at block #6,800,190 Β· updates every 60s
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