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Block #75,221

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/21/2013, 3:18:48 PM Β· Difficulty 8.9960 Β· 6,738,709 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
2f62adbd35eeccfd79f8eea466b8ff91e98cd48cc0a05eee682f232d949dc1b5
View on Chainz β†—

Height

#75,221

Difficulty

8.995979

Transactions

1

Size

203 B

Version

2

Bits

08fef87f

Nonce

625

Timestamp

7/21/2013, 3:18:48 PM

Confirmations

6,738,709

Merkle Root

5849ae3c3cc0630f68bd5025679228c6a39d7a5d48be831f161f86d061a39440
Transactions (1)
Coinbase5849ae3c3cc063…1f86d061a39440
1 in β†’ 1 out12.3400 XPM110 B
AWjCQh35…vvwZCGyU
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.

5.369 Γ— 10¹⁰²(103-digit number)
53692533780688826946…65793303740014575920
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
5.369 Γ— 10¹⁰²(103-digit number)
53692533780688826946…65793303740014575919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.369 Γ— 10¹⁰²(103-digit number)
53692533780688826946…65793303740014575921
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
1.073 Γ— 10¹⁰³(104-digit number)
10738506756137765389…31586607480029151839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.073 Γ— 10¹⁰³(104-digit number)
10738506756137765389…31586607480029151841
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
2.147 Γ— 10¹⁰³(104-digit number)
21477013512275530778…63173214960058303679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.147 Γ— 10¹⁰³(104-digit number)
21477013512275530778…63173214960058303681
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
4.295 Γ— 10¹⁰³(104-digit number)
42954027024551061556…26346429920116607359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.295 Γ— 10¹⁰³(104-digit number)
42954027024551061556…26346429920116607361
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
8.590 Γ— 10¹⁰³(104-digit number)
85908054049102123113…52692859840233214719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.590 Γ— 10¹⁰³(104-digit number)
85908054049102123113…52692859840233214721
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 75221

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 2f62adbd35eeccfd79f8eea466b8ff91e98cd48cc0a05eee682f232d949dc1b5

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 #75,221 on Chainz β†—
Circulating Supply:57,755,515 XPMΒ·at block #6,813,929 Β· updates every 60s
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