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Home/Chain Registry/Block #1,241,051

Block #1,241,051

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/17/2015, 6:00:23 PM Β· Difficulty 10.7559 Β· 5,554,836 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
8018fc4253e4666d63dea19d33201013f5db8b25d38579d36d7657c55554e305
View on Chainz β†—

Difficulty

10.755907

Transactions

1

Size

243 B

Version

2

Bits

0ac18319

Nonce

446,482,474

Timestamp

9/17/2015, 6:00:23 PM

Confirmations

5,554,836

Merkle Root

ab43516bdc347dd4b7ab9591c10b89b1cdeca554a17f23b4b524a3c05fe6882a
Transactions (1)
Coinbaseab43516bdc347d…24a3c05fe6882a
1 in β†’ 2 out8.6300 XPM152 B
APp2HX9W…jqfbWTPBALPu3s2c…EJXLjVFh
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.

1.531 Γ— 10⁹⁷(98-digit number)
15317475716128420832…26305539422811073280
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
1.531 Γ— 10⁹⁷(98-digit number)
15317475716128420832…26305539422811073279
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.531 Γ— 10⁹⁷(98-digit number)
15317475716128420832…26305539422811073281
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
3.063 Γ— 10⁹⁷(98-digit number)
30634951432256841665…52611078845622146559
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.063 Γ— 10⁹⁷(98-digit number)
30634951432256841665…52611078845622146561
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
6.126 Γ— 10⁹⁷(98-digit number)
61269902864513683331…05222157691244293119
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.126 Γ— 10⁹⁷(98-digit number)
61269902864513683331…05222157691244293121
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
1.225 Γ— 10⁹⁸(99-digit number)
12253980572902736666…10444315382488586239
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.225 Γ— 10⁹⁸(99-digit number)
12253980572902736666…10444315382488586241
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
2.450 Γ— 10⁹⁸(99-digit number)
24507961145805473332…20888630764977172479
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.450 Γ— 10⁹⁸(99-digit number)
24507961145805473332…20888630764977172481
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 1241051

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 8018fc4253e4666d63dea19d33201013f5db8b25d38579d36d7657c55554e305

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 #1,241,051 on Chainz β†—
Circulating Supply:57,611,179 XPMΒ·at block #6,795,886 Β· updates every 60s
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