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Block #234,322

TWNLength 9ā˜…ā˜†ā˜†ā˜†ā˜†

Bi-Twin Chain Ā· Discovered 10/30/2013, 6:25:28 AM Ā· Difficulty 9.9439 Ā· 6,561,291 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
cb987f8011e6c39c00951e495bf266c5256151c2670a668c7a702cccf8a21e91
View on Chainz ā†—

Height

#234,322

Difficulty

9.943854

Transactions

2

Size

869 B

Version

2

Bits

09f1a067

Nonce

199,827

Timestamp

10/30/2013, 6:25:28 AM

Confirmations

6,561,291

Mined by

ā›ļø P2SHAdTXMzeRsi3LZfFsqnrPjVGaoKtMnYeobf

Merkle Root

23cd5611662764fd0871d7a30611e55afbf727bea56660aa5ac46409ff6ea708
Transactions (2)
Coinbase3f8a1dd71bcaeaā€¦3049f7de456dbd
1 in ā†’ 1 out10.1100 XPM109 B
AdTXMzeRā€¦tMnYeobf
c619b5f39e8b57ā€¦25548bdcab13c5
4 in ā†’ 2 out129.4053 XPM670 B
AUhVF9jBā€¦XAbArZanAZZUuZYVā€¦MAUGyCNM
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) ā€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.312 Ɨ 10ā¹āµ(96-digit number)
13126010866905719446ā€¦00933308315557862399
Discovered Prime Numbers
Lower: 2^k Ɨ origin āˆ’ 1 | Upper: 2^k Ɨ 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 ā€” Twin Prime Pair (origin Ā± 1)
origin āˆ’ 1
1.312 Ɨ 10ā¹āµ(96-digit number)
13126010866905719446ā€¦00933308315557862399
Verify on FactorDB ā†—Wolfram Alpha ā†—
origin + 1
1.312 Ɨ 10ā¹āµ(96-digit number)
13126010866905719446ā€¦00933308315557862401
Verify on FactorDB ā†—Wolfram Alpha ā†—
Difference: origin + 1 āˆ’ origin āˆ’ 1 = 2 (twin primes āœ“)
Level 1 ā€” Twin Prime Pair (2^1 Ɨ origin Ā± 1)
2^1 Ɨ origin āˆ’ 1
2.625 Ɨ 10ā¹āµ(96-digit number)
26252021733811438893ā€¦01866616631115724799
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^1 Ɨ origin + 1
2.625 Ɨ 10ā¹āµ(96-digit number)
26252021733811438893ā€¦01866616631115724801
Verify on FactorDB ā†—Wolfram Alpha ā†—
Difference: 2^1 Ɨ origin + 1 āˆ’ 2^1 Ɨ origin āˆ’ 1 = 2 (twin primes āœ“)
Level 2 ā€” Twin Prime Pair (2^2 Ɨ origin Ā± 1)
2^2 Ɨ origin āˆ’ 1
5.250 Ɨ 10ā¹āµ(96-digit number)
52504043467622877786ā€¦03733233262231449599
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^2 Ɨ origin + 1
5.250 Ɨ 10ā¹āµ(96-digit number)
52504043467622877786ā€¦03733233262231449601
Verify on FactorDB ā†—Wolfram Alpha ā†—
Difference: 2^2 Ɨ origin + 1 āˆ’ 2^2 Ɨ origin āˆ’ 1 = 2 (twin primes āœ“)
Level 3 ā€” Twin Prime Pair (2^3 Ɨ origin Ā± 1)
2^3 Ɨ origin āˆ’ 1
1.050 Ɨ 10ā¹ā¶(97-digit number)
10500808693524575557ā€¦07466466524462899199
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^3 Ɨ origin + 1
1.050 Ɨ 10ā¹ā¶(97-digit number)
10500808693524575557ā€¦07466466524462899201
Verify on FactorDB ā†—Wolfram Alpha ā†—
Difference: 2^3 Ɨ origin + 1 āˆ’ 2^3 Ɨ origin āˆ’ 1 = 2 (twin primes āœ“)
Level 4 ā€” Twin Prime Pair (2^4 Ɨ origin Ā± 1)
2^4 Ɨ origin āˆ’ 1
2.100 Ɨ 10ā¹ā¶(97-digit number)
21001617387049151114ā€¦14932933048925798399
Verify on FactorDB ā†—Wolfram Alpha ā†—

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 ā€” the large number shown above ā€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

ā˜…ā˜†ā˜†ā˜†ā˜†
Rarity
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 Ɨ 3 Ɨ 5 Ɨ 7 Ɨ ā€¦), the result is the first prime in the chain. The origin is deliberately divisible by this primorial ā€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Ɨ Primorial (2Ā·3Ā·5Ā·7Ā·11Ā·ā€¦)
Source: Primecoin prime.cpp ā€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors ā€” 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 āˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,608,969 XPMĀ·at block #6,795,612 Ā· updates every 60s
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