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Block #907,097

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/23/2015, 9:13:37 PM Β· Difficulty 10.9350 Β· 5,905,329 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
58574a464d0c8008e5a11c312e9a4101aa76cefba1d0b9ae355e0e396c3dbe94
View on Chainz β†—

Height

#907,097

Difficulty

10.935033

Transactions

1

Size

208 B

Version

2

Bits

0aef5e53

Nonce

413,878,907

Timestamp

1/23/2015, 9:13:37 PM

Confirmations

5,905,329

Merkle Root

a7bb06a66ee2ac03d512a37d76653ef345b7ef61a33f3fadd993926cdfcdd994
Transactions (1)
Coinbasea7bb06a66ee2ac…93926cdfcdd994
1 in β†’ 1 out8.3500 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.

2.321 Γ— 10⁹⁹(100-digit number)
23215449101474648890…16913763113942056960
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
2.321 Γ— 10⁹⁹(100-digit number)
23215449101474648890…16913763113942056959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.321 Γ— 10⁹⁹(100-digit number)
23215449101474648890…16913763113942056961
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
4.643 Γ— 10⁹⁹(100-digit number)
46430898202949297780…33827526227884113919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.643 Γ— 10⁹⁹(100-digit number)
46430898202949297780…33827526227884113921
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
9.286 Γ— 10⁹⁹(100-digit number)
92861796405898595560…67655052455768227839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.286 Γ— 10⁹⁹(100-digit number)
92861796405898595560…67655052455768227841
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
1.857 Γ— 10¹⁰⁰(101-digit number)
18572359281179719112…35310104911536455679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.857 Γ— 10¹⁰⁰(101-digit number)
18572359281179719112…35310104911536455681
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
3.714 Γ— 10¹⁰⁰(101-digit number)
37144718562359438224…70620209823072911359
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.714 Γ— 10¹⁰⁰(101-digit number)
37144718562359438224…70620209823072911361
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 907097

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 58574a464d0c8008e5a11c312e9a4101aa76cefba1d0b9ae355e0e396c3dbe94

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 #907,097 on Chainz β†—
Circulating Supply:57,743,430 XPMΒ·at block #6,812,425 Β· updates every 60s
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