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Block #149,618

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/4/2013, 12:10:53 PM Β· Difficulty 9.8572 Β· 6,666,688 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e995e19218b5734e1cf6018170813411f1be69f821e77811708ca028b122ee82
View on Chainz β†—

Height

#149,618

Difficulty

9.857196

Transactions

2

Size

470 B

Version

2

Bits

09db7132

Nonce

176

Timestamp

9/4/2013, 12:10:53 PM

Confirmations

6,666,688

Merkle Root

40fbc40e3c2758e950ba4bb7a29f983515d90eb67666ae1c308e54015cf32134
Transactions (2)
Coinbase39c6b0a8c4e38c…77cd7b6e0ff53a
1 in β†’ 1 out10.2900 XPM109 B
ARwEjnek…XN12RHSr
952911ff27e1f1…72482b7aec4777
2 in β†’ 1 out20.6100 XPM272 B
AMm2NR1w…19uBFzE6
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.

3.485 Γ— 10⁹³(94-digit number)
34854304465783900818…72265263944924080000
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
3.485 Γ— 10⁹³(94-digit number)
34854304465783900818…72265263944924079999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.485 Γ— 10⁹³(94-digit number)
34854304465783900818…72265263944924080001
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
6.970 Γ— 10⁹³(94-digit number)
69708608931567801637…44530527889848159999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.970 Γ— 10⁹³(94-digit number)
69708608931567801637…44530527889848160001
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
1.394 Γ— 10⁹⁴(95-digit number)
13941721786313560327…89061055779696319999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.394 Γ— 10⁹⁴(95-digit number)
13941721786313560327…89061055779696320001
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
2.788 Γ— 10⁹⁴(95-digit number)
27883443572627120654…78122111559392639999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.788 Γ— 10⁹⁴(95-digit number)
27883443572627120654…78122111559392640001
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
5.576 Γ— 10⁹⁴(95-digit number)
55766887145254241309…56244223118785279999
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 149618

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 e995e19218b5734e1cf6018170813411f1be69f821e77811708ca028b122ee82

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 #149,618 on Chainz β†—
Circulating Supply:57,774,568 XPMΒ·at block #6,816,305 Β· updates every 60s
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