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Block #279,577

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/28/2013, 9:41:12 AM Β· Difficulty 9.9722 Β· 6,516,363 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
aae1886556b51c57b07bdbb77a00603f3ed86d637e426466ddbf85bdd85e8a9f
View on Chainz β†—

Height

#279,577

Difficulty

9.972157

Transactions

1

Size

210 B

Version

2

Bits

09f8df46

Nonce

7,429

Timestamp

11/28/2013, 9:41:12 AM

Confirmations

6,516,363

Merkle Root

7c65681d8cc1d749f81ec6545eba4cf0864950a408f20ff38e4b9bdd246d6dc9
Transactions (1)
Coinbase7c65681d8cc1d7…4b9bdd246d6dc9
1 in β†’ 1 out10.0400 XPM116 B
AcLBm5Z9…S683d7c3
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.

1.634 Γ— 10¹⁰⁴(105-digit number)
16348071238120573641…99153888415438602240
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
1.634 Γ— 10¹⁰⁴(105-digit number)
16348071238120573641…99153888415438602239
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.634 Γ— 10¹⁰⁴(105-digit number)
16348071238120573641…99153888415438602241
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
3.269 Γ— 10¹⁰⁴(105-digit number)
32696142476241147283…98307776830877204479
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.269 Γ— 10¹⁰⁴(105-digit number)
32696142476241147283…98307776830877204481
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
6.539 Γ— 10¹⁰⁴(105-digit number)
65392284952482294567…96615553661754408959
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.539 Γ— 10¹⁰⁴(105-digit number)
65392284952482294567…96615553661754408961
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
1.307 Γ— 10¹⁰⁡(106-digit number)
13078456990496458913…93231107323508817919
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.307 Γ— 10¹⁰⁡(106-digit number)
13078456990496458913…93231107323508817921
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
2.615 Γ— 10¹⁰⁡(106-digit number)
26156913980992917827…86462214647017635839
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.615 Γ— 10¹⁰⁡(106-digit number)
26156913980992917827…86462214647017635841
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 279577

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 aae1886556b51c57b07bdbb77a00603f3ed86d637e426466ddbf85bdd85e8a9f

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 #279,577 on Chainz β†—
Circulating Supply:57,611,609 XPMΒ·at block #6,795,939 Β· updates every 60s
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