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Block #162,660

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/13/2013, 11:20:38 AM Β· Difficulty 9.8614 Β· 6,662,058 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
789da8a670081fbb344dd51cc6a65794417df0998617bbbd29cbed29cf5d87e6
View on Chainz β†—

Height

#162,660

Difficulty

9.861415

Transactions

1

Size

199 B

Version

2

Bits

09dc85b2

Nonce

411,980

Timestamp

9/13/2013, 11:20:38 AM

Confirmations

6,662,058

Merkle Root

a06f568ba1fbbe686258e20e226368f578f432c240ac678ace2ef48e5ce87ad4
Transactions (1)
Coinbasea06f568ba1fbbe…2ef48e5ce87ad4
1 in β†’ 1 out10.2700 XPM109 B
AMLAAyBP…AobUBkWY
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.

5.055 Γ— 10⁹⁡(96-digit number)
50559079356511407895…53240438119693817600
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
5.055 Γ— 10⁹⁡(96-digit number)
50559079356511407895…53240438119693817599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.055 Γ— 10⁹⁡(96-digit number)
50559079356511407895…53240438119693817601
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
1.011 Γ— 10⁹⁢(97-digit number)
10111815871302281579…06480876239387635199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.011 Γ— 10⁹⁢(97-digit number)
10111815871302281579…06480876239387635201
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
2.022 Γ— 10⁹⁢(97-digit number)
20223631742604563158…12961752478775270399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.022 Γ— 10⁹⁢(97-digit number)
20223631742604563158…12961752478775270401
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
4.044 Γ— 10⁹⁢(97-digit number)
40447263485209126316…25923504957550540799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.044 Γ— 10⁹⁢(97-digit number)
40447263485209126316…25923504957550540801
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
8.089 Γ— 10⁹⁢(97-digit number)
80894526970418252632…51847009915101081599
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 162660

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 789da8a670081fbb344dd51cc6a65794417df0998617bbbd29cbed29cf5d87e6

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 #162,660 on Chainz β†—
Circulating Supply:57,841,810 XPMΒ·at block #6,824,717 Β· updates every 60s
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