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Block #75,753

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/21/2013, 6:34:33 PM Β· Difficulty 9.0387 Β· 6,725,282 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d0639d5c7d1c09317aaf12e1ea00f39f44ad97eabbb0d9e1de0b16436d7e89d2
View on Chainz β†—

Height

#75,753

Difficulty

9.038702

Transactions

1

Size

197 B

Version

2

Bits

0909e864

Nonce

445

Timestamp

7/21/2013, 6:34:33 PM

Confirmations

6,725,282

Merkle Root

6c2e7514c15429f5d5d61ef2c19e702de197495ab38dadf816cb57d5b29c73c8
Transactions (1)
Coinbase6c2e7514c15429…cb57d5b29c73c8
1 in β†’ 1 out12.2200 XPM110 B
AM8q6ydp…gok1vzFV
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.

1.309 Γ— 10⁸⁸(89-digit number)
13093798821627539081…26469308084561602240
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
1.309 Γ— 10⁸⁸(89-digit number)
13093798821627539081…26469308084561602239
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.309 Γ— 10⁸⁸(89-digit number)
13093798821627539081…26469308084561602241
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
2.618 Γ— 10⁸⁸(89-digit number)
26187597643255078162…52938616169123204479
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.618 Γ— 10⁸⁸(89-digit number)
26187597643255078162…52938616169123204481
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
5.237 Γ— 10⁸⁸(89-digit number)
52375195286510156325…05877232338246408959
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.237 Γ— 10⁸⁸(89-digit number)
52375195286510156325…05877232338246408961
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
1.047 Γ— 10⁸⁹(90-digit number)
10475039057302031265…11754464676492817919
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.047 Γ— 10⁸⁹(90-digit number)
10475039057302031265…11754464676492817921
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
2.095 Γ— 10⁸⁹(90-digit number)
20950078114604062530…23508929352985635839
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 75753

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 d0639d5c7d1c09317aaf12e1ea00f39f44ad97eabbb0d9e1de0b16436d7e89d2

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 #75,753 on Chainz β†—
Circulating Supply:57,652,344 XPMΒ·at block #6,801,034 Β· updates every 60s
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