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Block #160,971

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/12/2013, 8:10:16 AM Β· Difficulty 9.8598 Β· 6,656,378 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0860ebdade2fb6bcfcde816c6d8fb6b44ba17f4423faa90771d8366685564f25
View on Chainz β†—

Height

#160,971

Difficulty

9.859761

Transactions

1

Size

199 B

Version

2

Bits

09dc1946

Nonce

214,678

Timestamp

9/12/2013, 8:10:16 AM

Confirmations

6,656,378

Merkle Root

09386ff2cd5a0996a65db54051529e21afde1e49ce6eb54e8be46c94b0d63cb0
Transactions (1)
Coinbase09386ff2cd5a09…e46c94b0d63cb0
1 in β†’ 1 out10.2700 XPM109 B
AG9ocqwr…2MwsAk9z
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.

3.044 Γ— 10⁹³(94-digit number)
30440318750407980765…38998218103646455180
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
3.044 Γ— 10⁹³(94-digit number)
30440318750407980765…38998218103646455179
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.044 Γ— 10⁹³(94-digit number)
30440318750407980765…38998218103646455181
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
6.088 Γ— 10⁹³(94-digit number)
60880637500815961530…77996436207292910359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.088 Γ— 10⁹³(94-digit number)
60880637500815961530…77996436207292910361
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
1.217 Γ— 10⁹⁴(95-digit number)
12176127500163192306…55992872414585820719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.217 Γ— 10⁹⁴(95-digit number)
12176127500163192306…55992872414585820721
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
2.435 Γ— 10⁹⁴(95-digit number)
24352255000326384612…11985744829171641439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.435 Γ— 10⁹⁴(95-digit number)
24352255000326384612…11985744829171641441
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
4.870 Γ— 10⁹⁴(95-digit number)
48704510000652769224…23971489658343282879
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.870 Γ— 10⁹⁴(95-digit number)
48704510000652769224…23971489658343282881
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 160971

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 0860ebdade2fb6bcfcde816c6d8fb6b44ba17f4423faa90771d8366685564f25

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 #160,971 on Chainz β†—
Circulating Supply:57,782,839 XPMΒ·at block #6,817,348 Β· updates every 60s
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