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Block #573,120

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/2/2014, 12:40:53 PM Β· Difficulty 10.9666 Β· 6,230,883 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f135414275f66a5b629e975a9c8cf1ff2a14a1235b895d95ee2332041cb8922c
View on Chainz β†—

Height

#573,120

Difficulty

10.966597

Transactions

1

Size

209 B

Version

2

Bits

0af772e7

Nonce

4,873,933

Timestamp

6/2/2014, 12:40:53 PM

Confirmations

6,230,883

Merkle Root

4926be881bac20599dbf3326fe34673da2f7ae4b358e56ccbc8feef7e44ec4b7
Transactions (1)
Coinbase4926be881bac20…8feef7e44ec4b7
1 in β†’ 1 out8.3000 XPM116 B
ANSXnLY2…Sd25TjkD
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.

4.719 Γ— 10¹⁰⁰(101-digit number)
47195980775023829035…06728042531545415680
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
4.719 Γ— 10¹⁰⁰(101-digit number)
47195980775023829035…06728042531545415679
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.719 Γ— 10¹⁰⁰(101-digit number)
47195980775023829035…06728042531545415681
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
9.439 Γ— 10¹⁰⁰(101-digit number)
94391961550047658071…13456085063090831359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.439 Γ— 10¹⁰⁰(101-digit number)
94391961550047658071…13456085063090831361
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
1.887 Γ— 10¹⁰¹(102-digit number)
18878392310009531614…26912170126181662719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.887 Γ— 10¹⁰¹(102-digit number)
18878392310009531614…26912170126181662721
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
3.775 Γ— 10¹⁰¹(102-digit number)
37756784620019063228…53824340252363325439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.775 Γ— 10¹⁰¹(102-digit number)
37756784620019063228…53824340252363325441
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
7.551 Γ— 10¹⁰¹(102-digit number)
75513569240038126456…07648680504726650879
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.551 Γ— 10¹⁰¹(102-digit number)
75513569240038126456…07648680504726650881
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 573120

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 f135414275f66a5b629e975a9c8cf1ff2a14a1235b895d95ee2332041cb8922c

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 #573,120 on Chainz β†—
Circulating Supply:57,676,071 XPMΒ·at block #6,804,002 Β· updates every 60s
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