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Block #102,038

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/6/2013, 10:50:15 PM Β· Difficulty 9.4798 Β· 6,698,186 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9426d4b270834e7f4d5e41a283f7b53e24cdabdcc4613209f8a62396d360ac73
View on Chainz β†—

Height

#102,038

Difficulty

9.479790

Transactions

1

Size

200 B

Version

2

Bits

097ad37e

Nonce

37,182

Timestamp

8/6/2013, 10:50:15 PM

Confirmations

6,698,186

Merkle Root

1e621f6ba8b5fdfb5ba6f6c7a36f6dfe80cf3f57ecd6c75874e596d54e5acab6
Transactions (1)
Coinbase1e621f6ba8b5fd…e596d54e5acab6
1 in β†’ 1 out11.1100 XPM109 B
AGxyamTt…f4grrfx7
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.

1.179 Γ— 10⁹⁸(99-digit number)
11791424898845735515…05662030342010942460
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
1.179 Γ— 10⁹⁸(99-digit number)
11791424898845735515…05662030342010942459
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.179 Γ— 10⁹⁸(99-digit number)
11791424898845735515…05662030342010942461
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
2.358 Γ— 10⁹⁸(99-digit number)
23582849797691471030…11324060684021884919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.358 Γ— 10⁹⁸(99-digit number)
23582849797691471030…11324060684021884921
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
4.716 Γ— 10⁹⁸(99-digit number)
47165699595382942060…22648121368043769839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.716 Γ— 10⁹⁸(99-digit number)
47165699595382942060…22648121368043769841
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
9.433 Γ— 10⁹⁸(99-digit number)
94331399190765884121…45296242736087539679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.433 Γ— 10⁹⁸(99-digit number)
94331399190765884121…45296242736087539681
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
1.886 Γ— 10⁹⁹(100-digit number)
18866279838153176824…90592485472175079359
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 102038

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 9426d4b270834e7f4d5e41a283f7b53e24cdabdcc4613209f8a62396d360ac73

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 #102,038 on Chainz β†—
Circulating Supply:57,645,844 XPMΒ·at block #6,800,223 Β· updates every 60s
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