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Home/Chain Registry/Block #1,231,539

Block #1,231,539

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/11/2015, 9:05:05 AM Β· Difficulty 10.7387 Β· 5,583,573 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4a1e72b91bba95a5c3f6a29558234e0519e220a5cdcf3c8fcd486f24e73fa34d
View on Chainz β†—

Difficulty

10.738739

Transactions

1

Size

207 B

Version

2

Bits

0abd1dfd

Nonce

1,548,024,147

Timestamp

9/11/2015, 9:05:05 AM

Confirmations

5,583,573

Merkle Root

2f218fbb432f4fd5731a7510dfb42c3204e061e3ebea7b39860cb0dd2f602d5d
Transactions (1)
Coinbase2f218fbb432f4f…0cb0dd2f602d5d
1 in β†’ 1 out8.6600 XPM116 B
AJCEY9yy…tg97E6zm
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.

6.545 Γ— 10⁹⁢(97-digit number)
65455637756350729836…83199971144329116800
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
6.545 Γ— 10⁹⁢(97-digit number)
65455637756350729836…83199971144329116799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.545 Γ— 10⁹⁢(97-digit number)
65455637756350729836…83199971144329116801
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
1.309 Γ— 10⁹⁷(98-digit number)
13091127551270145967…66399942288658233599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.309 Γ— 10⁹⁷(98-digit number)
13091127551270145967…66399942288658233601
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
2.618 Γ— 10⁹⁷(98-digit number)
26182255102540291934…32799884577316467199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.618 Γ— 10⁹⁷(98-digit number)
26182255102540291934…32799884577316467201
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
5.236 Γ— 10⁹⁷(98-digit number)
52364510205080583869…65599769154632934399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.236 Γ— 10⁹⁷(98-digit number)
52364510205080583869…65599769154632934401
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
1.047 Γ— 10⁹⁸(99-digit number)
10472902041016116773…31199538309265868799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.047 Γ— 10⁹⁸(99-digit number)
10472902041016116773…31199538309265868801
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 1231539

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 4a1e72b91bba95a5c3f6a29558234e0519e220a5cdcf3c8fcd486f24e73fa34d

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 #1,231,539 on Chainz β†—
Circulating Supply:57,764,987 XPMΒ·at block #6,815,111 Β· updates every 60s
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