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Block #451,147

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/19/2014, 5:50:25 PM Β· Difficulty 10.3822 Β· 6,361,487 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b332762a0375af3a022021db06955c923318eb30a09c8ea4605fe2a85413a403
View on Chainz β†—

Height

#451,147

Difficulty

10.382170

Transactions

2

Size

391 B

Version

2

Bits

0a61d5e5

Nonce

124,035,728

Timestamp

3/19/2014, 5:50:25 PM

Confirmations

6,361,487

Merkle Root

db37601bb7eba8b6efe02f2d5e0a90677bd2da20eabea1700a9aa4e57f7340d8
Transactions (2)
Coinbase767fdd9ac6e9d3…f906b00e85dc56
1 in β†’ 1 out9.2700 XPM109 B
ARbkCSmH…GPH3qT3u
04f06773045235…225e775b17b7a0
1 in β†’ 2 out9.3100 XPM192 B
Ac7dbpaZ…XL2MrsxWALe73byb…gZoPcGoS
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.

5.048 Γ— 10⁹⁴(95-digit number)
50486887332065770034…57204379263729706320
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
5.048 Γ— 10⁹⁴(95-digit number)
50486887332065770034…57204379263729706319
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.048 Γ— 10⁹⁴(95-digit number)
50486887332065770034…57204379263729706321
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
1.009 Γ— 10⁹⁡(96-digit number)
10097377466413154006…14408758527459412639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.009 Γ— 10⁹⁡(96-digit number)
10097377466413154006…14408758527459412641
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
2.019 Γ— 10⁹⁡(96-digit number)
20194754932826308013…28817517054918825279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.019 Γ— 10⁹⁡(96-digit number)
20194754932826308013…28817517054918825281
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
4.038 Γ— 10⁹⁡(96-digit number)
40389509865652616027…57635034109837650559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.038 Γ— 10⁹⁡(96-digit number)
40389509865652616027…57635034109837650561
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
8.077 Γ— 10⁹⁡(96-digit number)
80779019731305232055…15270068219675301119
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.077 Γ— 10⁹⁡(96-digit number)
80779019731305232055…15270068219675301121
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 451147

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 b332762a0375af3a022021db06955c923318eb30a09c8ea4605fe2a85413a403

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 #451,147 on Chainz β†—
Circulating Supply:57,745,108 XPMΒ·at block #6,812,633 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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