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Block #241,492

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/3/2013, 6:04:58 AM Β· Difficulty 9.9580 Β· 6,591,836 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
709df4954656abac9e2b665f44e48f716566d6d5ee208f2f45537631fcab6710
View on Chainz β†—

Height

#241,492

Difficulty

9.957963

Transactions

1

Size

207 B

Version

2

Bits

09f53d10

Nonce

33,555,861

Timestamp

11/3/2013, 6:04:58 AM

Confirmations

6,591,836

Merkle Root

1f52920c36aad6bbb02be00ce812d431b18cbaaf2fbdf5c339c40f1910c3a079
Transactions (1)
Coinbase1f52920c36aad6…c40f1910c3a079
1 in β†’ 1 out10.0700 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.

3.819 Γ— 10⁹⁢(97-digit number)
38197082110314728144…67491481627491523680
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
3.819 Γ— 10⁹⁢(97-digit number)
38197082110314728144…67491481627491523679
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.819 Γ— 10⁹⁢(97-digit number)
38197082110314728144…67491481627491523681
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
7.639 Γ— 10⁹⁢(97-digit number)
76394164220629456288…34982963254983047359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.639 Γ— 10⁹⁢(97-digit number)
76394164220629456288…34982963254983047361
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
1.527 Γ— 10⁹⁷(98-digit number)
15278832844125891257…69965926509966094719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.527 Γ— 10⁹⁷(98-digit number)
15278832844125891257…69965926509966094721
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
3.055 Γ— 10⁹⁷(98-digit number)
30557665688251782515…39931853019932189439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.055 Γ— 10⁹⁷(98-digit number)
30557665688251782515…39931853019932189441
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
6.111 Γ— 10⁹⁷(98-digit number)
61115331376503565030…79863706039864378879
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 241492

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 709df4954656abac9e2b665f44e48f716566d6d5ee208f2f45537631fcab6710

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 #241,492 on Chainz β†—
Circulating Supply:57,910,817 XPMΒ·at block #6,833,327 Β· updates every 60s
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