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Block #134,158

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/25/2013, 9:59:37 PM Β· Difficulty 9.8011 Β· 6,692,573 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e7a1c00d5ab100f3b2980a6461c3157fa74cf1f4838b99879412f8134810d6c8
View on Chainz β†—

Height

#134,158

Difficulty

9.801117

Transactions

1

Size

198 B

Version

2

Bits

09cd15fd

Nonce

302,116

Timestamp

8/25/2013, 9:59:37 PM

Confirmations

6,692,573

Merkle Root

40f232b1f758b90e1ff775d1f094d90985138e16c0c1adcebfb204a7148f2822
Transactions (1)
Coinbase40f232b1f758b9…b204a7148f2822
1 in β†’ 1 out10.3900 XPM109 B
AVzQLNTE…s2g6CQPk
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.

2.315 Γ— 10⁹¹(92-digit number)
23150601150600193121…88848295813318721400
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
2.315 Γ— 10⁹¹(92-digit number)
23150601150600193121…88848295813318721399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.315 Γ— 10⁹¹(92-digit number)
23150601150600193121…88848295813318721401
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
4.630 Γ— 10⁹¹(92-digit number)
46301202301200386242…77696591626637442799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.630 Γ— 10⁹¹(92-digit number)
46301202301200386242…77696591626637442801
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
9.260 Γ— 10⁹¹(92-digit number)
92602404602400772485…55393183253274885599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.260 Γ— 10⁹¹(92-digit number)
92602404602400772485…55393183253274885601
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
1.852 Γ— 10⁹²(93-digit number)
18520480920480154497…10786366506549771199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.852 Γ— 10⁹²(93-digit number)
18520480920480154497…10786366506549771201
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
3.704 Γ— 10⁹²(93-digit number)
37040961840960308994…21572733013099542399
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 134158

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 e7a1c00d5ab100f3b2980a6461c3157fa74cf1f4838b99879412f8134810d6c8

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 #134,158 on Chainz β†—
Circulating Supply:57,858,002 XPMΒ·at block #6,826,730 Β· updates every 60s
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