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Block #113,129

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/12/2013, 8:57:51 AM Β· Difficulty 9.7294 Β· 6,711,901 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
60f8a3cabb640db2c4201be25a5e11e6bdb35b4fb7c51f8a74cd9a9a96fed5d6
View on Chainz β†—

Height

#113,129

Difficulty

9.729432

Transactions

1

Size

198 B

Version

2

Bits

09babc07

Nonce

14,541

Timestamp

8/12/2013, 8:57:51 AM

Confirmations

6,711,901

Merkle Root

dd08fc29d643951f206384febf0ad3ca28d96f01641b0878dc9e08f77f64b6f1
Transactions (1)
Coinbasedd08fc29d64395…9e08f77f64b6f1
1 in β†’ 1 out10.5500 XPM109 B
AJYjKv6M…8TXfzr5c
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.

7.126 Γ— 10⁹¹(92-digit number)
71260042812987689135…46917898436348324570
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
7.126 Γ— 10⁹¹(92-digit number)
71260042812987689135…46917898436348324569
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.126 Γ— 10⁹¹(92-digit number)
71260042812987689135…46917898436348324571
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
1.425 Γ— 10⁹²(93-digit number)
14252008562597537827…93835796872696649139
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.425 Γ— 10⁹²(93-digit number)
14252008562597537827…93835796872696649141
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
2.850 Γ— 10⁹²(93-digit number)
28504017125195075654…87671593745393298279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.850 Γ— 10⁹²(93-digit number)
28504017125195075654…87671593745393298281
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
5.700 Γ— 10⁹²(93-digit number)
57008034250390151308…75343187490786596559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.700 Γ— 10⁹²(93-digit number)
57008034250390151308…75343187490786596561
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
1.140 Γ— 10⁹³(94-digit number)
11401606850078030261…50686374981573193119
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 113129

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 60f8a3cabb640db2c4201be25a5e11e6bdb35b4fb7c51f8a74cd9a9a96fed5d6

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 #113,129 on Chainz β†—
Circulating Supply:57,844,323 XPMΒ·at block #6,825,029 Β· updates every 60s
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