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Block #75,758

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/21/2013, 6:37:20 PM Β· Difficulty 9.0392 Β· 6,736,858 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3d0d2f958ba70e89edb2e9e6918eb2628cde236c10718a12e478c7c5abecdf88
View on Chainz β†—

Height

#75,758

Difficulty

9.039166

Transactions

1

Size

204 B

Version

2

Bits

090a06cf

Nonce

132

Timestamp

7/21/2013, 6:37:20 PM

Confirmations

6,736,858

Merkle Root

d62ac0245c3cf0bed2da1c1119e2c6a77f8066929b20c52b7d71fc1e3d9131be
Transactions (1)
Coinbased62ac0245c3cf0…71fc1e3d9131be
1 in β†’ 1 out12.2200 XPM110 B
AecW7DS9…Kwvo1xJe
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.

7.236 Γ— 10¹⁰⁴(105-digit number)
72362251616663747933…58025051731250466840
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
7.236 Γ— 10¹⁰⁴(105-digit number)
72362251616663747933…58025051731250466839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.236 Γ— 10¹⁰⁴(105-digit number)
72362251616663747933…58025051731250466841
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
1.447 Γ— 10¹⁰⁡(106-digit number)
14472450323332749586…16050103462500933679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.447 Γ— 10¹⁰⁡(106-digit number)
14472450323332749586…16050103462500933681
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
2.894 Γ— 10¹⁰⁡(106-digit number)
28944900646665499173…32100206925001867359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.894 Γ— 10¹⁰⁡(106-digit number)
28944900646665499173…32100206925001867361
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
5.788 Γ— 10¹⁰⁡(106-digit number)
57889801293330998346…64200413850003734719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.788 Γ— 10¹⁰⁡(106-digit number)
57889801293330998346…64200413850003734721
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
1.157 Γ— 10¹⁰⁢(107-digit number)
11577960258666199669…28400827700007469439
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.157 Γ— 10¹⁰⁢(107-digit number)
11577960258666199669…28400827700007469441
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 75758

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 3d0d2f958ba70e89edb2e9e6918eb2628cde236c10718a12e478c7c5abecdf88

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 #75,758 on Chainz β†—
Circulating Supply:57,744,966 XPMΒ·at block #6,812,615 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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