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Block #113,123

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/12/2013, 8:55:09 AM Β· Difficulty 9.7293 Β· 6,713,983 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5572238683493c6395b3371a3ad3bf51befc716e7e7823d48d30d36be3620ae7
View on Chainz β†—

Height

#113,123

Difficulty

9.729273

Transactions

1

Size

201 B

Version

2

Bits

09bab1a0

Nonce

121,108

Timestamp

8/12/2013, 8:55:09 AM

Confirmations

6,713,983

Merkle Root

4797f93e8611b03cbba062121b89e44471ef0e1ac5a086c67575af3bab0e2baf
Transactions (1)
Coinbase4797f93e8611b0…75af3bab0e2baf
1 in β†’ 1 out10.5500 XPM109 B
AGNF5FM1…n54CJy51
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.

2.682 Γ— 10⁹⁹(100-digit number)
26821015188665465183…59276097271849728000
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
2.682 Γ— 10⁹⁹(100-digit number)
26821015188665465183…59276097271849727999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.682 Γ— 10⁹⁹(100-digit number)
26821015188665465183…59276097271849728001
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
5.364 Γ— 10⁹⁹(100-digit number)
53642030377330930367…18552194543699455999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.364 Γ— 10⁹⁹(100-digit number)
53642030377330930367…18552194543699456001
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
1.072 Γ— 10¹⁰⁰(101-digit number)
10728406075466186073…37104389087398911999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.072 Γ— 10¹⁰⁰(101-digit number)
10728406075466186073…37104389087398912001
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
2.145 Γ— 10¹⁰⁰(101-digit number)
21456812150932372147…74208778174797823999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.145 Γ— 10¹⁰⁰(101-digit number)
21456812150932372147…74208778174797824001
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
4.291 Γ— 10¹⁰⁰(101-digit number)
42913624301864744294…48417556349595647999
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 113123

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 5572238683493c6395b3371a3ad3bf51befc716e7e7823d48d30d36be3620ae7

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 #113,123 on Chainz β†—
Circulating Supply:57,861,026 XPMΒ·at block #6,827,105 Β· updates every 60s
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