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Block #251,071

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/8/2013, 7:57:21 PM Β· Difficulty 9.9694 Β· 6,573,812 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a7269382a8893c07424b5dce8bae5bfc2fa1937cca5673c4fe0880f341ed3174
View on Chainz β†—

Height

#251,071

Difficulty

9.969411

Transactions

1

Size

200 B

Version

2

Bits

09f82b4b

Nonce

209,881

Timestamp

11/8/2013, 7:57:21 PM

Confirmations

6,573,812

Merkle Root

23121f4ae06c88323c553fa10dd8006c3d510fd52245096f0fac8c6081d084be
Transactions (1)
Coinbase23121f4ae06c88…ac8c6081d084be
1 in β†’ 1 out10.0500 XPM109 B
AYr8ZrwV…Lcea3aHW
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.

3.327 Γ— 10⁹⁷(98-digit number)
33277605236390316754…97364250641456046080
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
3.327 Γ— 10⁹⁷(98-digit number)
33277605236390316754…97364250641456046079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.327 Γ— 10⁹⁷(98-digit number)
33277605236390316754…97364250641456046081
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
6.655 Γ— 10⁹⁷(98-digit number)
66555210472780633509…94728501282912092159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.655 Γ— 10⁹⁷(98-digit number)
66555210472780633509…94728501282912092161
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
1.331 Γ— 10⁹⁸(99-digit number)
13311042094556126701…89457002565824184319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.331 Γ— 10⁹⁸(99-digit number)
13311042094556126701…89457002565824184321
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
2.662 Γ— 10⁹⁸(99-digit number)
26622084189112253403…78914005131648368639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.662 Γ— 10⁹⁸(99-digit number)
26622084189112253403…78914005131648368641
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
5.324 Γ— 10⁹⁸(99-digit number)
53244168378224506807…57828010263296737279
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 251071

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 a7269382a8893c07424b5dce8bae5bfc2fa1937cca5673c4fe0880f341ed3174

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 #251,071 on Chainz β†—
Circulating Supply:57,843,146 XPMΒ·at block #6,824,882 Β· updates every 60s
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