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Block #237,847

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/1/2013, 6:33:03 AM Β· Difficulty 9.9506 Β· 6,563,013 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a448d25d95ea801330bca56a1c178a7f9e260e19888edcf7377779377dea6dbb
View on Chainz β†—

Height

#237,847

Difficulty

9.950638

Transactions

1

Size

208 B

Version

2

Bits

09f35d02

Nonce

66,597

Timestamp

11/1/2013, 6:33:03 AM

Confirmations

6,563,013

Merkle Root

a915627eede6f89ed1b227e9c1f89547109a88613f3b0af7c012abdaddbc3b7e
Transactions (1)
Coinbasea915627eede6f8…12abdaddbc3b7e
1 in β†’ 1 out10.0800 XPM116 B
AcLBm5Z9…S683d7c3
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.

1.732 Γ— 10⁹⁸(99-digit number)
17326000670899162554…65144316090619390620
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
1.732 Γ— 10⁹⁸(99-digit number)
17326000670899162554…65144316090619390619
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.732 Γ— 10⁹⁸(99-digit number)
17326000670899162554…65144316090619390621
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
3.465 Γ— 10⁹⁸(99-digit number)
34652001341798325108…30288632181238781239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.465 Γ— 10⁹⁸(99-digit number)
34652001341798325108…30288632181238781241
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
6.930 Γ— 10⁹⁸(99-digit number)
69304002683596650217…60577264362477562479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.930 Γ— 10⁹⁸(99-digit number)
69304002683596650217…60577264362477562481
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
1.386 Γ— 10⁹⁹(100-digit number)
13860800536719330043…21154528724955124959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.386 Γ— 10⁹⁹(100-digit number)
13860800536719330043…21154528724955124961
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
2.772 Γ— 10⁹⁹(100-digit number)
27721601073438660087…42309057449910249919
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.772 Γ— 10⁹⁹(100-digit number)
27721601073438660087…42309057449910249921
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 237847

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 a448d25d95ea801330bca56a1c178a7f9e260e19888edcf7377779377dea6dbb

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 #237,847 on Chainz β†—
Circulating Supply:57,650,942 XPMΒ·at block #6,800,859 Β· updates every 60s
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